There are several ways to calculate interest on a loan, of which two methods are most common: the declining balance method and the flat (face-value) method. Interest is generally paid over the term of the loan, although it is sometimes paid up front. These methods are discussed in detail in Annexe

The declining balance method

This method calculates interest as a percentage of the amount outstanding over the loan term.

Interest calculated on the declining balance means that interest is charged only on the amount that the borrower still owes. The principal amount of a one-year loan, repaid weekly through payments of principal and interest, reduces or declines every week by the amount of principal that has been repaid (table I). This means that borrowers have use of less and less of the original loan each week, until at the end of one year when they have no principal remaining and have repaid the whole loan (assuming 100 percent repayment).

For example, by month 6 of a 12-month loan for 1,000, the borrower will only owe approximately 500 if she or he has paid in regular weekly installments. At that point, she or he is paying interest on only 500 rather than 1,000. (Note that with interest paid on the declining balance, a greater portion of the monthly payment is paid in interest during the early months of the loan and a greater portion of principal is paid toward the end of the loan. This results in a slightly larger amount than half of the principal remaining outstanding at the mid- point of the loan. In the example in table I, in month six 524.79 is still outstanding, not 500.)

To calculate interest on the declining balance, a financial calculator is required. On most financial calculators, present value and payment must he entered with opposite signs, that is if present value is positive, payment must he negative, or vice versa. This is because one is a cash inflow and one is a cash outflow. Financial calculators allow the user to enter different loan variables as follows:

PV = Present value, or the net amount of cash disbursed to $c borrower at the beginning of the loan.

i = Interest rate, which must be expressed in some time units as n below.

n = loan term, which must equal the number of payments to be made,

PMT = Payment mode each period.

In the example above, a one-year loan of 1,000 with monthly payments and 20 percent interest calculated on the declining balance is computed by entering the following:

PV = -1,000 (enter as negative amount, as it is 0 cash outflow)

I = 20 percent per year; 1.67 percent a month

n = 12 months

Solve for PMT:

PMT = 92.63

Total payments equal 1,111,56 (12 months at 92.63). Total interest is 111.56. The declining balance method is used by most, if not all, formal financial institutions. It is considered the most appropriate method of interest calculation for MFI’s as well.

The flat rate method

This method calculates interest as a percentage of the initial loan amount rather than the amount outstanding (declining) during the loan term. Using the flat method means that interest is always calculated on the total amount of the loan initially disbursed, even though periodic payments cause the outstanding principal to decline. Often, but not always, a flat rate will be stated for the term of the loan rather than as a periodic (monthly or annual) rate. If the loan term is less than 12 months, it is possible to annualise the rate by multiplying it by the number of months or weeks in the loan term, divided by 12 or 52 respectively.

To calculate interest using the flat rate method the interest rate is simply multiplied by the initial amount of the loan. For example, if an MFI charges 20 percent interest using the flat rate method on a 1,000 loan, the interest payable is 200 (table 2).

It is clear that the actual amount of interest charged varies significantly depending on whether the interest is calculated on the declining balance or the flat amount. The flat method results in a much higher interest cost than the declining balance method based on the same nominal rate. In the example in table 2, interest of 200 (20 percent flat basis) is 88.44 or 80 percent greater than interest of 111.56 (20 percent declining balance).

To increase revenue some MFI’s will change the interest rate calculation method from declining balance to flat rather than increase the nominal rate. This may be in reaction to usury laws imposing a maximum rate of interest that is not high enough to cover the MFI's costs. However, MFI’s should realise that regardless of the nominal rate quoted, clients are well aware of how much interest they are actually paying, based on the amount due each payment period. It is important that all interest calculations he transparent.

These examples show that with all other variables the same, the amount of interest paid on a declining balance loan is much lower than that on a loan with interest calculated on a flat basis. To compare rates of interest calculated by different methods it is necessary to determine what interest rate would be required when interest is calculated on the declining balance to earn the same nominal amount of interest earned on a loan with a flat basis calculation.

In example 1, a 1,000 loan with 20 percent interest calculated on a declining balance for one year with monthly payments results in interest of 112 (rounded from 111.56). The same loan with interest calculated on flat basis results in interest of 200. To earn interest of 200 on a loan of 1,000 with interest calculated on the declining balance, the interest rate would have to increase by 15 percentage points to 35 percent (additional interest revenue of 88). Interest on a 1,000 loan at 35 percent declining balance results in monthly payments of 99.96 for one year or a total interest cost of 200 (rounded from 199.52).

This example shows that an MFI calculating interest on the declining balance would have to increase its nominal interest rate substantially to earn the same revenue as an MFI calculating interest on a flat basis.

How Do Fees or Service Charges Affect the Borrower and the MFI?

In addition to charging interest, many MFI’s also charge a fee or service charge when disbursing loans. Fees or service charges increase the financial costs of the loan for the borrower and revenue to the MFI. Fees are often charged as a means of increasing the yield to the tender instead of charging nominal higher interest rates.

Fees are generally charged as a percentage of the initial loan amount and are collected up front rather than over the term of the loan. Because fees are not calculated on the declining balance, the effect of an increase in fees is greater than a similar increase in the nominal interest rate (if interest is calculated on the declining balance).

In example 2, the MFI wants to determine its future pricing policy. In doing so, it wants to calculate die effect on the borrower of an increase in the interest rate and, alternatively, an increase in the loan fee.

In example 1 a 20 percent interest rate (declining balance) on a 1,000 loan resulted in 112 in interest revenue. A loan fee of 3 percent on this loan would result in a fee of 30, making total revenue 142. The MFI wants to increase its rate by 5 percentage points either through the loan fee it charges (from 3 percent to 8 percent) or the interest rate it charges (from 20 percent to 25 percent declining balance). Each increase results in the following:

Total revenue collected on a 1,000 loan with 20 percent interest (declining balance) and an 8 percent fee equals 192 (112 +:80). Total revenue collected on a 1,000 loan with 25 percent interest (declining balance) and a 3 percent fee equals 170 (140 + 30). The effect of a 5 percentage point increase in the loan fees from 3 percent to 8 percent is greater than a 5 percent age point increase in the interest rate, provided interest is calculated on the declining balance. This is because the fee is charged on the initial loan amount whereas the interest is calculated on the declining balance of the loan.

Although the interest rate may be the same nominal figure, the costs to the borrower-and hence the yield to the lender-vary greatly if interest is calculated on a flat basis or if fees are charged. This will be discussed further in the section below on calculating effective rates of interest.

Calculating Effective Rates

MFI's often speak about the "effective interest rate" on their loans. However, there are many ways in which effective rates are calculated, making it very difficult to compare institutions’ rates. The effective rate of interest is a concept useful for determining whether the conditions of a loan make it more or less expensive for the borrower than another loan and whether changes in pricing policies have any effect Because of the different loan variables and different interpretations of effective rates, a standard method of calculating the effective rate on a loan (considering all variables) is necessary to determine the true cost of borrowing for clients and the potential revenue (yield) earned by the MFI.

The effective rate of interest refers to the inclusion of all direct financial costs of a loan in one interest rate. Effective interest rates differ from nominal rates of interest by incorporating interest, fees, the interest calculation method, and other loan requirements into the financial cost of the loan. The effective rate should also include the cost of forced savings or group fund contributions by the borrower, because these are financial costs. We do not consider transaction costs (the financial and non-financial costs incurred by the borrower to access the loan, such as opening a bank account, transportation, child-care costs, or opportunity costs) in the calculation of the effective rate, because these can vary significantly depending on the specific market. However, it is important to design the delivery of credit and savings products in a way that minimises transaction costs for both the client and the MFI.

When interest is calculated on the declining balance and there are no additional financial costs to a loan, the effective interest rate is the same as the nominal interest rate. Many MFIS, however, calculate the interest on a flat basis, charge fees as well as interest, or require borrowers to maintain savings or contribute to group funds (trust or insurance funds). The cost to the borrower is, therefore, not simply the nominal interest charged on the loan but includes other costs. Consideration must also be given to the opportunity cost of not being able to invest the money that the borrower must pay back in regular instalments (the time value of money).

Variables of microloans that influence the effective rate include:

When all variables are expressed as a percentage of the loan amount, a change in the amount of the loan will not change the effective rate. A fee that is based in currency (such as R25 per loan application) will change the effective rate if the loan amount is changed; that is, smaller loan amounts with the same fee (in currency) result in a higher effective rate.

Calculation of the effective rate demonstrates how different loan product variables affect the overall costs and revenues of the loan. Two methods of calculating the effective rate of interest are an estimation method, which uses a formula that does not require a financial calculator, and the internal rate of return method.

Note that the estimation method does not directly take into account the time value of money and the frequency of payments, which are considered in the internal rate of return method. Although the difference may be minimal, the greater the length of the loan term and the less frequent the loan payments, the more substantial the difference will be. This is because the longer the loan is outstanding and the less frequent the payments, the greater the effect on the cost will be and hence the difference between the estimated effective cost and the internal rate of return calculation, In addition, the estimation method does not take into account compulsory savings or contributions to other funds, such as trust or insurance funds. It is presented here simply as a method for calculating the effective rate if no financial calculator or spreadsheets are available.

Estimating the Effective Rate

If you do not have access to a financial calculator or a computer spreadsheet, you can compute an estimation of the effective rate. The estimation method considers the amount the borrower pays in interest and fees over the loan term. The estimation method can be used to determine the effect of the interest rate calculation method, the loan term, and the loan fee. An estimation of the effective rate is calculated as follows.

Effective cost = Amount paid in interest and fees divided by Average principal amount outstanding

Note: Average principal amount outstanding (Sum of principal amounts outstanding) divided by number of payments

To calculate the effective cost per period, simply divide the resulting figure by the number of periods.

As previously illustrated, the amount of interest revenue is largely affected by whether interest is calculated on a flat or declining balance basis. With all other variables the same, the effective rate for a loan with interest calculated on a declining balance basis will he lower than the effective rate for a loan with interest calculated on a flat basis.

Using an example similar to that in tables 1 and 2, the effective rate is estimated for a 1,000 loan with interest of 20 percent and a 3 percent fee, first with interest calculated on the declining balance and then with interest calculated on the flat basis. Calculating the interest on the declining balance results in an estimated annual effective rate of 25 percent or 2.1 percent per month. Calculating the interest on a flat basis results in an estimated annual effective rate of 42 percent or 3.5 percent per month.

With all other factors the same, the effective rate increases from 25 percent (2.1 percent per month) to 42 percent (3.5 percent per month) when the method of calculation is changed from declining balance to flat. The effective rate also increases when the loan term is shortened if a fee is charged. This is because fees are calculated on the initial loan amount regardless of the length of the loan term. If the loan term is shortened, the same amount of money needs to be paid in a shorter amount of time, thus increasing the effective rate. This difference is greatest when a fee is charged on a loan with interest calculated on the declining balance. This is because the shorter loan term increases the relative percentage, of the fee to total costs. The effective rate can be estimated for a number of loan variables, including an increase in the loan fee and a decrease in the loan term. Note that the effect of an increase in the fee by 5 percent (to 8 percent) has the same effect (an increase of 0.8 percent per month in effective rate) whether the loan is calculated on a declining basis or flat method. This is because the fee is calculated on the initial loan amount.

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[1] Several texts exist that cover interest rate calculations. In this report we use a standard text as base and to ensure that we do not compare different methods. The text used is Ledgerwood, Joanna. (1999). Microfinance Handbook: An institutional and a financial perspective. Published by Sustainable Banking with the Poor Project, The World Bank, Washington DC.