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The authors present empirical evidence that borrowers, consciously or not, leave traces of their intentions, circumstances, and personality traits in the text they write when applying for a loan. This textual information has a substantial and significant ability to predict whether borrowers will pay back the loan above and beyond the financial and demographic variables commonly used in models predicting default. The authors use text-mining and machine learning tools to automatically process and analyze the raw text in over 120,000 loan requests from Prosper, an online crowdfunding platform. Including in the predictive model the textual information in the loan significantly helps predict loan default and can have substantial financial implications. The authors find that loan requests written by defaulting borrowers are more likely to include words related to their family, mentions of God, the borrower’s financial and general hardship, pleading lenders for help, and short-term-focused words. The authors further observe that defaulting loan requests are written in a manner consistent with the writing styles of extroverts and liars.

Loan guarantee schemes have existed since 1953 (in the US) and are widely used throughout the world to provide financial support to smaller firms by guaranteeing loans from commercial banks. The UK government has been an active supporter of loan guarantees since 1981, and has a long track record of modifying its scheme to reflect changing market conditions and the financing needs of its SME sector. Arguably the two most significant changes occurred in 2008 when the 5-Year Rule on eligibility was removed and in 2009 when the long-standing Small Firms Loan Guarantee Scheme was replaced by the Enterprise Finance Guarantee Scheme. We treat the removal of the 5-Year Rule as a natural policy experiment and empirically question whether, on economic grounds, this was a sensible policy. Our findings suggest that the 5-Year Rule was a better policy choice with regard to employment but had no impact on sales growth.

Regulation of credit use by individuals is as old as human history. Sometimes, however, rationales for aspects of regulations become lost in history to the point that current policy debates about them contain elements of mythology. Nowhere is this truer among kinds of consumer credit than for small cash installment loans. The origin of these loans as consumer protection under the Uniform Small Loan Law is often largely forgotten, and policy debates over their current regulation often betray misunderstandings. This paper discusses a group of such beliefs in a number of areas: reasons for using credit in the first place, interest rate ceilings on loans, lending profitability, loan renewals, Rule of 78s, and credit insurance. It seems that good public policy would benefit from less attention to mythology and more to actual experience.

Previous studies have highlighted the question of government loan interest as one of great current importance. Government borrowing levels are high, and reducing interest payments would generate savings to meet other spending needs and/or to lower taxation, thus supporting the sustainability of public finances. However, no previous study has presented a method for a local government to calculate its own credit risk and thus be in a position to negotiate lower interest rates on its borrowing. This article defines a financial model that enables local governments to estimate the interest rate payable on a bank loan, based on their credit risk premium, in accordance with the Basel II rules and the findings of our empirical study of large local governments.

We construct a synthesized model to study credit rationing by loan size. In our model, the borrower faces a trade-off between raising debt and exerting costly effort to undertake an investment project. In the absence of agency costs, increasing the loan size at the equilibrium interest rate raises the default risk and hence reduces the average cost of the loan for the borrower, so the borrower always demands a larger loan than what the lender can offer. Furthermore, agency cost raises this excess demand for a given interest rate. If the agency cost is sufficiently high, the borrower is unable to obtain the loan that she needs at any interest rate, requiring the use of non-price instruments in the loan contract. This is the common logic underlying the agency models of non-price credit rationing, as we show in the cases of costly state verification, money diversion, risk-shifting and hidden shirking.

This paper analyzes how the movements of the policy interest rate affect bank-relevant variables through changes in the composition of the loan portfolio. Using a computational approach that fully accounts for borrowers’ heterogeneity, we show how the variety of bank customers changes and how this change affects the bank's cash influx, making it more volatile. The paper also sheds light on how the composition of the loan portfolio is affected by an increase in the policy interest rate when it is kept at low levels. Safer borrowers exit the loan portfolio first, causing a gradual increase in the loan portfolio risk. The interest payment influx shrinks because riskier borrowers repay less often. Furthermore, we find that a shortening of the lending time horizon increases the volatility clustering of the bank interest payment influx.

During periods of high interest rates, businesses utilize their own capital, merge with other businesses, or diversify, and borrow when it is absolutely necessary. People also avoid hardship through refinancing during economic slowdowns because interest rates are low enough to recover some of their income and lower debt interest. High interest rates are more inviting to investments although hard to sustain in the long run. The future looks grim and interest rates have been down for a while, and will probably stay down for some time to come. This paper investigates ways to lower the earnings percentage in interest rates. A new set of the uniform series of the future worth of money involving linear gradients will be mathematically reformulated to investigate the possibility of lowering the interest rate for long term loans and mortgages. A new equation will be formulated and put into a tabulated practical example.

Lending and borrowing money are ancient practices with specific injunctions for dealing with the borrower given in the Bible. In modern times loans allow the borrower to acquire goods in advance while the lender earns profit through the interest charged. Interest-loaded loans may lead to overspending with financially disastrous consequence for the borrower. In this paper, two models of loan payment, Equal Principal Payment (Model 1) and Equal Installment Payment (Model 2 are presented based on diminishing balance interest rate. The simulated results of the models compared with data provided by a private credit cooperative showed Model 2 to be more realistic, the amount paid comparable with payment to the Credit Cooperative and easy to remember. The interest charged by the private cooperative fluctuated but in a declining pattern while the interest charged in the two models declined continuously, with lesser total interest charged but the difference is not significant. Understanding interest schemes for loan payments may mitigate the danger of financial disaster through overspending.  Keywords: Mathematical model, interest, equal installment payment, equal principal payment

Investors borrow money from banks and other financial institutions. The response of investment expenses changes keenly with interest rate which is at the mind of money-making analysis. Interest rates is the other strong factors that affect financial policies as well as weaker financial payments in guiding principles of investors, it facilitate investment if the high interest rate is applicable on savings. Interest rate influences savings practically all commercial banks commencing macroeconomic theories. The negative influence of higher investment rate inhibits the macroeconomic effect of interest rate policy. Interest rate is the money charged on loan of money. Investors borrow money from banks for investment. As a result of this encouragement, the bank lenders are competent to attain repayment of each and every loan by means of high prospect. As soon as it comes in the direction of mortgage contracts (if a borrower discards mortgage repayment), the loan official once more plays the central role by means of warning as well as if necessary authorize non-payment clients. Apart from the danger of advertising the security within a small number of days, they can slash off borrowers commencing extra way in to loans. The response of investment expenses changes with interest rates of having a loan from banks. The main objective of the study was to investigate the effect of interest rates on business investment performance. The specific objectives of the study was to find out the effects of cash lending on business investment, to evaluate the effects of loan repayment of on business investment performance and to examine the outcome of domestic savings on business investment performance. The literature review was viewed from other related studies. The conceptual framework had two variables according to the topic under study. The independent variable was interest rate and dependent variables were business investment. The study area was in Kisii town. The target population was all employees of 18 commercial banks more so branch managers, head of units and credit managers. The researcher was select 6 commercial banks to represent 30% of the target population 18 commercial banks. The systematic stratified sampling was used to get the sample size which was arrived at through census and it comprised of 482 respondents of commercial banks. The data were collected by questionnaires as the research instruments. Data were analyzed by the use of descriptive statistics and it was presented the analyzed in figures and frequency tables. The study wanted to investigate whether loan repayment affect investment performance the determinant of credit analysis used before granting cash services to the clients. The findings showed that there was influence of loan repayment on financial performance in banks. The study wanted to indicate techniques of credit analysis used before granting credit services to the investment and found out that Firm undertakes legal action for clients who fails to repay with the least mean of the evaluation is done on credit worthiness of clients and determinants of loan repayment in microcredit are still debatable among different researchers that might be due to situational factors like country level factors, bank level factors and the condition of legal and regulatory framework of the country. Thus, these debates can only be resolved through quantitative analysis on the determinants of loan repayments. The study suggested for further studies.

A common situation is where a borrower is offered the choice of two types of loans—a fixed interest rate loan for a fixed period or a variable interest (floating interest) rate loan. Usual wisdom and advice is that the borrower opts for the fixed rate loan if interest rates are anticipated to rise in the future or opts for the variable rate loan if interest rates are anticipated to fall. However, depending on the magnitude of the rates offered, and the rate uncertainty in the market, such wisdom may not always be well founded. This note demonstrates why this might be. It derives a readily usable, low-mathematical-background expression showing, for borrowers, when fixed and variable rate loans are equivalent and when one rate type is better/worse than the other.

Dyskusja nad kondycją współczesnych mikrofinansów skupia się na wielu problemach, wśród których ważne miejsce zajmuje zagadnienie warunków dostępu do usług mikrofinansowych, w tym oprocentowania produktów pożyczkowo-kredytowych. Przekonaniu, że stopy procentowe kredytów udzielanych osobom ubogim powinny być dla nich na tyle „atrakcyjne”, aby produkty te mogły być wykorzystywane przez swoich beneficjentów, przeciwstawia się koncepcję, zgodnie z którą stopa ta musi być kalkulowana, przede wszystkim, na poziomie zapewniającym trwałość i stabilność funkcjonowania instytucji mikrofinansowej, nawet w sytuacji konieczności stosowania wysokich cen usług finansowych, często przekraczających poziomy wyznaczane dla oprocentowania kredytów/pożyczek oferowanych przez tradycyjnych pośredników finansowych. Te sprzeczne poglądy tworzą przestrzeń rozważań prowadzonych w niniejszym artykule, którego celem jest określenie i analiza uwarunkowań determinujących oprocentowanie mikropożyczki, zarówno w wymiarze teoretycznym, jak i praktycznym, oraz przedstawienie własnych, autorskich refleksji dotyczących powyższej problematyki.

Usury laws cap the interest rates that lenders can charge. Using data from Prosper.com (an online lending marketplace), I show how interest rate caps affect: 1) the probability that a loan is funded; 2) the amount a borrower requests; 3) the interest rate at which a loan is funded; and 4) loan repayments. The key to my empirical strategy is that there initially was substantial variability in states' interest rate caps, according to which Prosper borrowers from different states faced caps ranging from 6 to 36%. A behind-the-scenes change in loan origination, however, suddenly increased the cap to 36% in all but one state. This change, which was not pre-announced, creates \treatment" states where caps rose and a few control states where caps remained unchanged. I find that higher interest rate caps increase the probability that a loan will be funded, especially if the borrower is risky and previously was just \outside the money." I do not find, however, that borrowers change the loan amounts they request or that their probability of default rises. On the other hand, the interest rate paid rises slightly, probably because online lending is substantially, yet imperfectly, integrated with the general credit market.

The common-law in duplum rule, as it is generally known in South African law, provides that interest stops running when unpaid interest equals the outstanding capital amount. If the total amount of unpaid interest (both contractual and default interest: our courts apply the limitation to both kinds of interest: see Stroebel v Stroebel 1973 (2) SA 137 (T) and Administrasie van Transvaal v Oosthuizen & 'n Ander 1990 (3) SA 387 (W)) has accrued to an amount equal to the outstanding capital sum, the defaulting debtor (ie, the borrower of the money) must first start making payments on his loan again (and so decrease the interest amount), after which interest may once again accrue to an amount equal to the outstanding capital sum. The rule thus effectively prevents unpaid interest from accruing further once it reaches the unpaid capital sum. Even if interest is capitalised (and interest is therefore charged on interest), the capitalised interest does not lose its character as interest and become part of the capital amount for purposes of applying the in duplum rule (see Standard Bank of SA Ltd v Oneanate Investments (Pty) Ltd 1995 (4) SA 510 (C), in particular at 560 and 566-72; confirmed on appeal in Standard Bank of South Africa Ltd v Oneanate Investments (Pty) Ltd (in liquidation) 1998 (1) SA 811 SCA; unless otherwise indicated, all further references to Standard Bank v Oneanate Investments will be to the decision on appeal).

This research paper aims to analyze the credit risk involved in peer-to-peer (P2P) lending system of “LendingClub” Company. The P2P system allows investors to get significantly higher return on investment as compared to bank deposit, but it comes with a risk of the loan and interest not being repaid. Ensemble machine learning algorithms and preprocessing techniques are used to explore, analyze and determine the factors which play crucial role in predicting the credit risk involved in “LendingClub” publicly available 2013–2015 loan applications dataset. A loan is considered “good” if it's repaid with interest and on time. The algorithms are optimized to favor the potential good loans whilst identifying defaults or risky credits.

Personal loans can be obtained by borrowers from very different types of lending institution. The most common are a traditional loan institutions, payday lenders, or a Peer to Peer (P2P) lending brokers. P2P lending companies do not loan the money directly. They link the borrower to a lender and provide the lender with the borrower’s income which is not usually verified. The P2P lenders collects fees based on the transaction and financially benefits from a higher number of introductions of borrowers and lenders. P2P lending is becoming more popular among borrowers because the pay highest interest rates are much lower than payday lenders and loans require less verification of income and assets than traditional loan institutions. A higher reported income with P2P lenders can result in a larger loan for the borrower and thus more profit and fees generated for the P2P lender. If the loan defaults due to an overstated or fraudulently reported income by the borrow, the P2P lender does not suffer, it is the lender that was matched to the borrower by the P2P lender that will incur the financial loss. This paper focuses on proposing a data science approach to detecting loan applicants that provide fraudulent income data to P2P lenders. The data obtained for this study contained 887,379 observations and 74 variables of loan applicants from the P2P loan company, Lending Club. The initial observations of this data showed that unverified loans make up 23% of the defaulted loans while verified and source verified loans made up about 77%. Described within this paper is how the data set for analysis was obtained and prepared for analysis, the initial findings, the proposed data science approach to fully analyzing this data, and the significance of the lending industry, both traditional and P2P, with a method of detecting fraudulent income reported on loan applications. Models generated from this analysis could be incorporated by lenders into their applications along with research in this area should improve the P2P lending industry by increasing the detection of fraudulent income reported on loan applications.

Our country generally has voluntarily buys custom of the room, but house price actually non- each individual people all can bear its amount, therefore all relies on the mortgage loan which the financial organ provides. However the financial organ after the loaning out fund, will be able to face the loan person in also the funds behavior irregularity, will break a contract the situation influence to be biggest, further inquired into its influence factor has its necessity. Breaks a contract influence factor the situation to be possible to differentiate for the interest rate with the non- interest rate two aspects, tended to by the recent years market rate undulation relaxes the tendency to look, analysis the non- interest rate influence factor appeared is important. This research directly embarks from the loan characteristic, the analysis contains the loan amount, the loan interest rate, period of payments and so on three variables to break a contract influence the situation, and returns (Logistic Regression , LR) the model makes the real diagnosis analysis, the real diagnosis result also demonstrated the non- interest rate influence factor reveals the influence to the loan person irregular also funds behavior existence.

Three large banks control over half of the U.S. commercial loan market by volume through the syndication process. Using attributes of a borrower's location to instrument for lender-- borrower matching, I show that the borrower stock price response to a loan announcement is more favorable if one of these dominant banks is the lender, especially if the borrower is "opaque." I then show that these banks charge lower interest rates and are more likely to lend without the protection of a borrowing base. The results suggest that the dominant banks have a particularly high reputation for screening and monitoring borrowers. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

In a roll-up mortgage, the borrower receives a loan in the form of a lump sum. The loan is rolled up with interest until the borrower dies, sells the house, or moves into long-term care permanently. The house is sold at that time, and the proceeds are used to repay the loan and interest. Most roll-up mortgages are sold with a no-negative-equity guarantee (NNEG), which caps the redemption amount at the lesser of the face amount of the loan and the sale proceeds. The core of this study is to develop a framework for pricing and managing the risks of the NNEG.

From the perspective of Chinese commercial banks' loan pricing, combined with credit rationing theory, using the method of agent-based computational finance(ACF), to do the bank loan's simulation experiment both on “one cutting” type of interest rate pricing and a comprehensive pricing model. From the comparison, we found that the different interest rates pricing model impact SMEs loan. From the experiment when the loan interest rate raise to a certain extent, the earning of bank will reduce accompany by the increasing of interest rate, to some extent, reflecting the credit rationing phenomenon of SMEs(Small and Medium Enterprises). Through the experiment we found that the comprehensive loan interest rate pricing method slow down their financing difficulties, and they also don't reduce bank's earning. So the commercial banks should choose a reasonable interest rate pricing model, according to the loan amount, credit grade, asset-liability ratio, the way of security, and other indicators, according to the risk of small, low cost, and the specific circumstances of the borrower companies, to implement different interest rate.

In fact, most credit card issuers (or home equity banks) frequently offer cardholders (or customers) a teaser interest rate (say, I 1 ), which is significantly lower than the regular interest rate of I 2 (with I 2 > I 1 ) for only 6 months or a year (say, M 2 ) to lure new customers from their competitors. Consequently, the customer faces a progressive interest charge from the bank. If the customer pays the outstanding balance by the grace period (say, M 1 which is generally 25 days), then the bank does not charge any interest. If the outstanding amount is paid after M 1 , but by M 2 (with M 2 > M 1 ), then the bank charges the customer the teaser interest rate of I 1 on the unpaid balance. If the customer pays the outstanding amount after M 2 , then the bank charges the regular interest rate of I 2 . In this paper, we first establish an appropriate EOQ model for a retailer when the bank (or the supplier) offers a progressive interest charge, and then provide an easy-to-use closed-form solution to the problem.

The aging problem became more important and serious in China in recent years. The reverse mortgage is an innovation model to support the aged people. In this study, the accumulation function model of interest force with a Wiener process and a negative-binomial distribution is proposed as the basis for the reverse mortgage. With the proposed model, a lump sum pricing model, annuity pricing model, linear increasing annuity pricing model for single-life and double-lives are provided. All of the models can be improved to solve the problem that the actuarial pricing models of reverse mortgage only could be calculated by the fixed interest rate. LS : The amount of the loan which is got by one borrower with a method of payment with the stochastic interest rate. ' PMT : The amount of the loan which is got by one borrower at the beginning of each year with the method of annuity under the stochastic interest rate. ' PMTA : The amount of the loan which is got by one borrower at the beginning of the first year by linear increasing annuity with the stochastic interest rate. Q: The increasing amount every year of the loan when get the loan by linear increasing annuity. d: The increasing ratio every year of the loan when get the loan by equal ratio increasing annuity. xy LS ' : The amount of the loan which is got by two borrowers by a sum of loan ceiling with the stochastic interest rate. xy PMT ' : The amount of the loan which is got by two borrowers at the beginning of each year by annuity with the stochastic interest rate. xy

We consider a model of lending with subsequent loan sale opportunities. Market participants observe a public signal about the creditworthiness of each borrower. Lenders additionally have the opportunity to privately screen potential borrowers at a cost. The model rationalizes empirically documented discontinuities in lending and default rates around a FICO credit rating score of 620, while providing a foundation for the endogenous emergence of a cutoff rule-of-thumb. We show that loan sale opportunities have a positive impact on borrowers' access to credit contingent on screening revealing positive information whenever the public information about a borrower's type is relatively bad. At the same time, average borrower quality for intermediate borrower types decreases as gains from trade via loan sales increase the relative profitability of loans to unscreened borrowers compared to loans to screened borrowers which imply significant risk retention. Loan sale opportunities can lead to adverse effects on borrower welfare while strictly increasing lender profitability.

Investors in private equity funds make payments for fund management fees and for fund investments; they receive capital which comes from the sale of these investments and that capital is net of carried interest. The carried interest is non-zero if the fund has returned sufficient capital back to the investor (and is zero otherwise). The calculation of the carried interest is complex and investors usually do not track the total amount of carried interest accrued. This means that investors cannot have a historical and comprehensive perspective on carried interest. However, because carried interest is paid only if performance is good, it is commonly thought that tracking carried interest does not matter anyway. Yet, because this fee is non-linear and investors have a portfolio of funds, significant carried interest can be paid even when the private equity portfolio has shown poor performance. This means that tracking carried interest is economically useful. Data from three large US pension funds is used to illustrate. Statistics are remarkably similar across these investors. Estimated carried interest is about $5 billion, which represents about 13% of capital invested, 19% of overall profit and 38% of profits above a standard benchmark (8% per annum over four year). Given past performance, past carried interest paid does not appear to be a major issue. Yet, the conclusion depends on the benchmark used, the estimated absolute amount of carried interest is significant, and if future performance differs from past performance, the way carried interest is currently computed could be problematic for investors going forward.

The theory of financial intermediation assigns banks a unique role in the resolution of information asymmetry. Banks, in general, obtain private information about the borrower and the project during the screening of loan applicants and during the monitoring of loan recipients. Incumbent banks, in particular, utilize information obtained while monitoring previous loan extensions to resolve information asymmetry when granting subsequent loans. We examine the rate on a sequence of loans to a borrower and find that the incumbent bank information advantage has finite magnitude and is quickly reflected in the pricing of the second loan. We also find that the lending relationship does not deteriorate to the detriment of the borrower. This study also provides further evidence supporting the hypothesis that an incumbent bank resolves information asymmetry during the monitoring of loan extensions.

This article provides an arbitrage-free model to evaluate the term structure of lending interest rates when a fraction of collateral is recovered upon default of the borrower. Unlike the previous literature, we assume that the value of the collateral asset fluctuates over time with certain correlation to the risk-free interest rate as well as the default hazard rate of the borrower. It is shown that the bank loan is a sum of holding a coupon-bearing bond and selling a put option, both being callable upon default. A Gaussian model is considered, as a special case, to derive an analytic expression of the appropriate lending interest rates, and some numerical example is given to demonstrate that bank loans exhibit different properties from corporate bonds.

This paper analyzes optimal loan interest rate contracts under conditions of risky, symmetric information for one-period (static) and multi-period (dynamic) models. The optimal loan interest rate depends upon the volatility of, and co-variation among the market interest rate, borrower collateral, and borrower income, as well as the time horizon and the risk preferences of lenders and borrowers. For a risk-averse borrower with stochastic collateral, variable interest rate contracts are, in general, Pareto optimal. For plausible assumptions, the optimal loan interest rate for the multi-period model often exhibits “muted” responses to changes in market interest rates, making fixed rate loans a reasonable approximation for the optimal loan. Hence, in the absence of optimal contracts, long-term (short-term) borrowers tend to prefer fixed rate (variable) contracts.

Particularly in Japan, risk management relating to bankruptcy of financed enterprises has become very important to a bank after the collapse of a bubble economy. To obtain suitable revenues, a bank has to apply high interest rates to the enterprises with high risk. When enterprises which have made a secure loan from a bank go bankrupt, a bank forecloses such enterprises from its mortgage to recover the loss incurred. However, in actual circumstances, it may need much cost and effort to do so in Japan. This paper proposes a stochastic model to determine an adequate interest rate, taking account of the probabilities of bankruptcy and mortgage collection, and their costs. Numerical examples are given to illustrate this model and a loan interest rate is determined.

Interest rate risk is a major concern for banks because of the nominal nature of their assets and the asset-liability maturity mismatch. This paper proposes a new way to derive a bank's interest rate sensitivity, by examining separately the effects of interest rate changes on existing loans(loans-in-place) and potential loans (loans-in-process). A potential loan is shown to be equivalent to an American option to lend, and is valued using option theory. An increase in interest rates generally has a negative effect on existing loans. However, if both deposit and lending rates rise by the same amount, the value of a potential loan generally increases. Hence a bank's lending slack (or ratio of loans-in-process to loans-in-place) will determine its overall interest rate risk. Empirical evidence indicates that low-slack banks indeed have significantly more interest rate risk than high-slack banks. The model also makes predictions regarding the effect of deposit and lending rate parameters on bank credit availability. Empirical tests with quarterly data are generally supportive of these predictions.

A new model for predicting the future expected cash flows from a loan is developed. It is based on a detailed analysis of the events of fulfilling, delinquency and default of each individual payment on the loan. The proposed model has significantly less uncertainty compared with the Markov chain model with the same detailing. The model is expected to have greater predictive power in comparison to the traditional models, and its usage will allow reducing the interest rate on the loan. The results of estimation of the probabilities of payments over time and the future expected cash flows from the loan with monthly equal principal repayment are given.

We develop a simple model of competition in a loan market with no asymmetric information. Lenders compete by offering loan contracts which are a loan amount and an interest rate. A borrower may take up more than one contract and has an incentive to default which is increasing in the amount that she has borrowed. We show that if the incentive to default is high enough then firms in competition earn a positive profit and may even charge the monopoly price. In the latter case, the aggregate quantity in the market is equal to the amount a monopolist would provide. Further, there is a level of incentive to default above which no zero profit equilibria can be sustained. The positive profit equilibria are robust to increases in the number of lenders in the market. We argue that this model is appropriate for markets in which transactions are on credit rather than cash and in particular explains some of the stylized facts of the credit--card market. Our model implies that, given a choice of bankruptcy laws, consumers prefer strict bankruptcy laws and banks prefer lenient ones.

Commercial loan borrowers meet random cash needs via multi-period loans from the bank, but fluctuations in interest rates may justify paying off some outstanding loans before they mature. The objective is to minimize the expected present value of the interest and prepayment penalties paid to the bank subject to a liquidity constraint. From Chiang (2005), it is shown that a firm should not inventory cash if contingent opportunities are ignored. By extending her article, it is also found that if a borrower is not risk neutral, a more risk-averse borrower prepays a larger amount.

The current economic and financial crisis situation, in general, and the real-estate crisis, in particular, have favoured the introduction of new banking products, especially loans, which, on the one hand, try to make the investment in housing attractive through novel mortgage loans and, on the other hand, to adapt to the possible financial difficulties of the borrower. In effect, lot of families need to have a house, but the banks are afraid that the borrower punctually could not face the corresponding payments. In this case, some financial entities give the borrower the possibility of deferring some payments until the end of the loan term, under the conditions which will be detailed hereinafter. In this paper, we present a mathematical expression of the average duration of the loan and the value of the payment that would amortize the loan in the initially stipulated period.

This paper studies the optimal nominal policy interest rate in a model with the cost channel and imperfect competition in the banking sector. Due to this market power, the interest rate on deposits is relatively low; in particular it is lower than the policy interest rate. This, in turn, leads to a suboptimal level of deposits and, as a result, to a low level of intermediation. Deviations from the Friedman Rule are optimal in this setup regardless of the assumption about price rigidity; since households can hold their assets in the form of cash or deposits, taxing money, which is an imperfect substitute for deposits, is optimal in order to increase the level of deposits and encourage intermediation. They main results of the paper are robust to the introduction of market power in the loan market as well as stickiness in both the deposit and the loan markets.

This paper analyzes a model of bank loan repayment as a signalling game. The model has shown that under asymmetric information a borrower reaches for renegotiation and debt forgiveness to a greater extent than is required by the return of the project financed with loan. In the equilibrium the borrower pays the lesser of an amount equal to the liquidation value or the amount of payment specified in the credit agreement. To offset the impact of the renegotiation options, interest rate specified in the loan agreement should ex ante take into account the liquidation value of the borrower's assets. The paper also proposes an example of utilisation of our theoretical model and the Monte Carlo method to determine the loan interest rate for a commercial loan.

In this chapter we consider an important commercial application of compound interest and equations of value, namely loans . In particular, we discuss how to calculate regular repayment amounts and methods for calculating the loan outstanding at any time within the term of the loan. The chapter ends with a brief discussion of alternative definitions of the interest rates that can occur in commercial practice.

We report the results from a field experiment with a micro lender in Uganda to test the effectiveness of privately implemented incentives for loan repayment. Using a randomized control trial we measure the impact of three different treatments: Borrowers are either given a lump sum cash reward upon completion of the loan (equivalent to a 25% interest rate reduction on the current loan), a 25% reduction of the interest rate in the next loan the borrower takes from the bank, or a monthly text message reminder before the loan payment is due (SMS). We find that on average the size of the treatment effect is similar across all the treatment groups: borrowers in the treatment groups have a 7-9% increase in the probability of paying on time and the average days late drop by 2 days a month. The results suggest that simple text messages which help borrowers to better manage their repayment dates have similar effects as large changes in the cost of capital of 25% of interest. The impact of the cash back incentives are stronger for customers with smaller loans and less banking experience, the reduced future interest rate seemed to be most effective for customers with larger loans, while the SMS text messages were particularly effective for younger customers.

I Introduction MONEYLENDING in the rural areas of South Asia takes various forms. One type of informal loan agreement commonly found in many areas is the usufructuary land mortgage, hereinafter abbreviated to ULM. Under this type of contract, the borrower transfers to the lender a parcel of his land, to be held by the latter as collateral until the exact monetary amount of the loan is repaid in full. In all cases, after the loan is made, the lender is in possession of the collateral with the authority to cultivate or lease out the land. In this type of loan, the lender, the mortgagee, charges no explicit interest on the loan. However, because the mortgagee is free to utilize the land for his own cultivation, income from the land is, in effect, an implicit form of interest.(1) The repayment period for the principal is not specified when the loan is contracted--the landowner is free to reclaim his land as soon as he has the means to pay back the loan. In practice, the land is held for a few years. Field research shows that at least four to five years usually elapse before a loan is repaid, and the average repayment period is much longer than that (Bertocci, 1972; Rashid, 1983). Under some arrangements, the title of the mortgaged land is also transferred to the lender with a verbal stipulation that when the loan is repaid, the land title would revert to the borrower. In such cases, the lender becomes the owner of the land in legal terms and acquires all usufruct rights, including the right to sell. However, social sanctions deter sale of collateral unless the borrower is in default. While there is no stated term for the loan, default and foreclosure are relevant and meaningful concepts in the context of ULM. However, these concepts cannot be interpreted in purely legalistic terms. Foreclosure can occur for a variety of reasons. For example, if a borrower expresses his inability or unwillingness to repay the loan, he forfeits the collateral. On the other hand, a lender can foreclose if a borrower is deemed to be in default. A not too uncommon foreclosure scenario involves a majlish (gathering) or shalish (arbitration) of village elders. If the elders make a determination that the borrower has no chance of redemption owing to his worsening financial conditions, or other reasons, the land belongs to the lender, de jure as well as de facto. One interesting thing to note is that if, as in some cases, the borrower is given the title to the land when the loan is made, foreclosure proceedings take place only for social validation of the transfer of ownership. The literature on rural credit has largely focused on the determinants of the high rate of interest on loans (Bhaduri, 1973; Long, 1968; Wai, 1958). Many have noted, in passing, that collaterals, including land, are often undervalued by the lender in loan contracts (Wai, 1958; Bottomley, 1963b; Bhaduri, 1977). Since providing an explanation for the high rate of interest has been the prime concern, the collaterals and their valuation have not always been integrated in the analyses. In this paper, the informal credit market and usufructuary land mortgage is examined from two points of view: to seek the rationale for the undervaluation of collateral, and to explore the implications of the undervaluation for the determination of interest rates for secured loans. Contrary to the literature which sees undervaluation of collaterals, and thus the high interest rates, as attributable to risk and monopoly power (see Section II below), this paper provides a model that shows the proper relationship between undervaluation of collaterals and the high implicit rates of interest on ULMs. This relationship only can be understood by comparing the opportunity cost of funds and return from money-lending: The opportunity cost of funds tied up in loans is equal to the net income foregone, including capital gains, from comparable pieces of land, whereas return from moneylending is given by net income from the land collateral, after factoring in default. …

It is commonly known that, as of January 1, 1991, changes have taken place in the conditions for repaying housing loans issued at favorable rates of interest. The trade publications paid almost no attention to this topic, and the dailies and weeklies did not even explain such important categories as the real (present) value of the loan or the weighted mean time of servicing the loan. Thus even basic mathematical relationships have not been explained. The primary aim of this article is to remedy these shortcomings. It describes how mortgage payments and the amount of total debt depend on the loan, the length of repayment, and the interest rate. It presents the actual value of the loan and the weighted mean time of servicing the loans. It analyzes the comparative advantages and disadvantages of the laws proposed by the government and the one ratified by the National Assembly. Finally, it gives a brief sketch of a methodically preferable way of servicing loans that indexes the mortgage payment instead of the interest.

The basic variables involved in the mathematical formulation of an instalment loan are the amount of the loan, the number of instalments in the term of the loan, the size of each payment and the interest rate on the loan (commonly referred to as the annual percentage rate or APR). Given any three of these variables, the fourth can be calculated with the aid of annuity tables. The underlying relationship is, however, quite complex and it is therefore difficult to gain analytical understanding of the interplay between the variables, especially in view of the fact that the functional dependence of the APR on the remaining variables cannot be explicitly stated. An approximate formula for the APR is derived in terms of a lower bound which is shown to be quite sharp provided the finance charge per unit financed is less than one. On the basis of this formula, several analytical results are derived. In particular, the rates of change characteristics of the payment size with respect to the loan amount and to the i...

In social lending, in which an individual lends or borrows money using an SNS network, a person who lends money must take a risk that the money won't be returned. Since social lending is a comparatively new field, very few studies have been made. Therefore, we present an experimental assessment of the influence of the updating of an interest rate using Bayesian estimation, which takes into consideration the influence of groups with agents. Our method decreases dispersions of the delay of the borrower in payment with the increasing loan history of the borrower. As a result, when the lenders are risk-averse (risk means the dispersions of the delay of the borrower at each interest rate), the number of transactions increases. Therefore, our method is effective because it can cause the transactions of lenders who are risk-averse to increase.

The rule of 78s is a scheme for the repayment of debts which is used by some banks and finance companies. The rule employs uniform periodic payments, but differs from the competing conventional repayment method in that the interest rate is not constant, but rather is greater than average initially and then declines throughout the life of the loan. The effect is that the lender is laying early claim to interest payments and consequently the unpaid balance is corresponding larger. Important formulas for the rule of 78s are developed. An example is presented.

Fueled by significant press scrutiny, the tax treatment of "carried interests" has generated intense controversy in the tax academy and on Capitol Hill. Carried interests are profit shares granted to investment fund managers in exchange for services. Under current law, wealthy fund managers often report the income from the compensatory carried interest at the low 15% capital gains rate. This has provoked the recent outrage since ordinary workers pay tax on their compensation at regular rates as high as 35%. In response, Representative Levin recently proposed a bill which would tax fund managers at the higher 35% rate on all their fund earnings. While this response initially appeals as a matter of basic fairness, we believe that deeper analysis exposes several fatal defects in the Levin Proposal. In contrast to others who critique the Levin proposal, however, we similarly reject the do-nothing status quo. We advocate instead a more moderate legislative fix. Under our approach, the increased tax rate would apply to only a portion of the carried interest return, equal to a fixed rate of interest on the investors' capital subject to the carried interest. As discussed below, this narrowed application has strong theoretic appeal. It also provides a practical middle-ground compromise between the two extremes of the Levin Proposal and the status quo. The carried interest is best analyzed as an implicit loan to the manager since the manager receives the full profits from the invested capital subject to the carried interest. From this perspective, the taxable compensation is limited to the lack of interest on the "loaned" capital. Despite some recognition of its theoretic appeal, no commentator has yet to advocate adoption of the interest charge approach. We believe that several missing pieces to the analysis, including our key modification to the approach, explain its failure to gain traction. In contrast to other commentators, we would grant the manager an interest expense allowance for any foregone interest on the loaned capital. Our adjustment provides desirable consistency with the treatment of an actual interest-free loan. It also avoids an undesirable double taxation of the foregone interest (once as compensation, and a second time upon the fund's actual realization of the carried interest profit). We grant this interest expense allowance in reliance upon an existing, but under appreciated, provision that permits "investment interest" expense to be deducted only against "investment income." This significant limitation insures that the compensation from the carried interest will be taxed at the desired higher rates since it blocks use of the interest expense against the reportable compensation. In sum, our approach makes sound economic sense and favorably treats the implicit carried interest loan the same as an actual interest-free loan. The Levin proposal goes overboard in taxing the carry more harshly than an actual loan. Current law misses the mark in the other direction by taxing the carry more lightly than an explicit loan. Finally, our modified approach also contains other benefits over the Levin Proposal. For instance, the Levin Proposal increases the "tax lock-in" effect over what it is under current law by increasing the tax rate on the managers' realized carry profits. Our proposal favorably avoids this increase by maintaining the low capital gains rate on the realized carry profits.

This paper investigates the effect of personal characteristics and the way people present themselves on their likelihood of getting a loan, the terms of such loan, and whether these characteristics are correlated with future loan performance. After controlling for credit score, credit history, income, employment status, and homeownership, personal characteristics like beauty, race, appearing creditworthy, being overweight, or the context of the picture a borrower posts significantly affect the likelihood of getting a loan and/or the interest rate paid. Beautiful borrowers are 1.41 percent more likely to get a loan and pay 81 basis points less than an average-looking borrower with the same credentials. Black borrowers pay between 139 and 146 basis points more than an otherwise similar White borrower. The borrower's personal characteristics do not appear to be significantly related to subsequent delinquency rates, with the exception of beauty that, all else equal, makes a borrower more than three times as likely to become delinquent. I also find that lenders' sophistication and personal characteristics such as gender, race, age and income affect their lending decisions. Similarity between borrowers and lenders also has a statistically significant and large economic effect on the terms of the loan, although it doesn't change the impact of the other explanatory variables. The setting of the study is a large U.S. online lending website.

The paper presents a model of a bank loan repayment as a signaling game with a set of discrete types of borrowers. The type of the borrower is the return on investment project. A possibility of renegotiation of the loan agreement leads to an equilibrium in which the borrower adjusts repaid amount to the liquidation value of its assets from the bank’s point of view. In the equilibrium there are numerous pooling equilibrium points with values rising according to the expected liquidation value of the loan. The article additionally proposes mechanism forcing the borrower to pay all of his return instead of the common liquidation value of subset of types of the borrower. The paper contains also a simple numerical example explaining this mechanism.

In this paper, I exploit the syndicated loan market to explore the impact of information asymmetry on the cost of debt capital. As a measure of information asymmetry associated with a borrowing firm, I use the bid-ask spread on the firm’s loans traded on the secondary loan market. I find that a higher bid-ask spread on a borrower’s traded loans leads to a higher interest rate on the borrower’s subsequently issued loans. I show that both information asymmetry between syndicate lenders and a borrowing firm and information asymmetry among secondary loan market participants are priced in the loan interest rate. I also find that information asymmetry decreases debt maturity. I show that a higher bid-ask spread on the borrower’s traded loans translates into a shorter maturity of the borrower’s subsequently issued loans.

We rationalize fixed rate loan commitments (forward credit contracting with options) in a competitive credit market with universal risk neutrality. Future interest rates are random, but there are no transactions costs. Borrowers finance projects with bank loans and choose ex post unobservable actions that affect project payoffs. Credit contract design by the bank is the outcome of a (non-cooperative) Nash game between the bank and the borrower. The initial formal analysis is basically in two steps. First, we show that the only spot credit market Nash equilibria that exist are inefficient in the sense that they result in welfare losses for borrowers due to the bank's informational handicap. Second, we show that loan commitments, because of their ability to weaken the link between the offering bank's expected profit and the loan interest rate, enable the complete elimination of informationally induced welfare losses and thus produce an outcome that strictly Pareto dominates any spot market equilibrium. Perhaps our most surprising result is that, if the borrower has some initial liquidity, it is better for the borrower to use it now to pay a commitment fee and buy a loan commitment that entitles it to borrow in the future rather than save it for use as inside equity in conjunction with spot borrowing.

Publisher Summary This chapter discusses various methods of computing accrued interest, when it applies in a bond trade, and the different conventions in calculating accrued interest. Accruing interest on bond trades is simply a trade custom. In the United States, accrued interest is added to the price, and the buyer pays the total, consisting of two separate parts. For trades done at a dollar price, the accrued interest would be added, and the total becomes the total amount paid. However, the accrued interest could also be included in the bond price. Not all bonds accrue interest. Bonds that are in default are traded at a dollar price, without an accrued interest. This is because the bonds are in default, so they are not paying either principal or interest.

Publisher Summary This chapter introduces the concept of interest as payment for the use of capital, first in the money form, with examples. It presents the equation for calculating simple interest and expands the interest concept to the notion of return on investment, with a wide variety of examples. The examples are particularly meant to make the readers aware of the various places where they can use a financial analysis. Interest is payment for the use of capital, usually in the form of money. The traditional equation for interest computation is: Interest = Principal*Rate*Time. This is called “simple interest.” The interest rate is often expressed as a percentage rather than a decimal. The interest rate description must contain both a rate and the time-period to which that rate applies.

Most papers studying loan guarantee are under a one-borrower and one-guarantor framework. This study uses the option approach to construct models in which loan guarantees are analyzed under a multiple-borrower and one-guarantor framework and under a one-borrower and multiple-guarantor structure with stochastic interest rates. We carry out simulations to investigate how the important parameters of borrowers and guarantors affect the values and default probability of loan guarantees. Our results show that the correlation parameters play a critical role in determining the premiums of loan guarantee portfolios and joint loan guarantees.