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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.

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.

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.

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.

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.

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

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.

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.

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.

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 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.

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.

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.

This paper evaluates alternative rules by which the Fed may set interest rates using the small model of the U.S. economy estimated in Rotemberg and Woodford (1997). Our main substantive finding is that low and stable inflation together with stable interest rates can be achieved by letting the funds rate respond positively to inflation while also responding, with a coefficient bigger than one, to the lagged funds rate itself. A rule in which the interest rate is set in this extremely simple way does almost as well as a more complicated rule which is optimal in our setting, in the sense of maximizing expected utility to the representative household. Furthermore, when the funds rate responds to inflation only with a delay, due to delay in the availability of inflation data, performance under the rule is only slightly reduced.

The purpose of this article is to provide an in-depth explication of basic concepts and operational precepts of the rule of seventy-eights sol that the accountant may better understand and, therefore, better advise his client in regard to interest income recognition. This income recognition technique does have wide application and as will be shown, is a theoretically valid approach to recording interest revenue so long as certain constraints are not violated.

An installment loan is an arrangement between a lender of money and a borrower in which the lender gives the borrower a fixed sum of money called the loan principal which he expects will be repaid in a specified number of equal periodic payments. The process of repaying a loan in installments is called amortization. As in most loan agreements, the borrower pays a fixed rate of interest on the outstanding balance of the unpaid principal. Each fixed periodic payment is the sum of two parts: the interest payment calculated as described and the principal payment equal to the difference between the fixed total payment and the interest payment. Thus part of each payment goes toward paying off the total interest and part toward paying off the loan itself. The sum of all interest payments is called the finance charge; the sum of all principal payments is the loan principal. Example 1. A $1,000 loan is to be repaid in 12 monthly installments of equal size. The interest rate is 18% per year or 1.5% per month. From standard amortization tables (Ref. 5) or by algebraic formula (shortly to be derived) the required fixed monthly payment is $91.68. Table 1 is a table of payments and balances by month as the loan progrssses. It was necessary to reduce the final payment to $0.02 in order to force the final balance to be zero. The adjustment is necessitated by rounding errors. The loan principal, number of payments, and interest rate are the loan assumptions from which the fixed monthly payment, finance charge, and all other variables are derived.

A previous paper [Arvan and Brueckner (1986)] showed that in an optimal loan contract, interest rate risk should be shared between lender and borrower, with the slope of the loan-rate function (which relates the loan interest rate to the lender's uncertain cost-of-funds) lying between zero and one. Existing adjustable-rate mortgage (ARM) contracts violate this rule since they require complete risk absorption by the borrower when interest rate caps are not binding. The present paper shows that when the earlier model is modified by adding a second type of borrower, efficient loan contracts look more like existing ARMs.

THIS PAPER IS concerned with the role of interest rates, down-payments, and contract maturities in the allocation of mortgage funds among borrowers. It has been widely observed that decreases in interest rates on mortgage and other consumer loans' are often accompanied by decreases in average down-payments and increases in average contract maturities.2 The most popular explanation for this association is one variant of the credit-rationing hypothesis that might best be called the "multiple-term hypothesis." Lenders, so this argument goes, do not ration funds solely on the basis of price-the interest rate-but also on the basis of other conditions of the loan, requiring higher down-payments or shorter maturities than (some) borrowers would prefer to arrange at the quoted interest rate. When either the demand for loans falls or supply increases, lenders may reduce rates charged but also allow borrowers more generous terms in the form of lower downpayments or longer maturities.8 Likewise, according to this argu