Mifos supports the following types of interest calculation; flat interest rate, declining balance, declining balance interest with equal principal installments, and declining balance with interest recalculation. Flat and declining balance types both result in Equal Monthly Installments (EMI). Declining balance interest with equal principal installments allow MFIs to calculate interest using equal principal installments, and simple declining balance formula to calculate the interest.

P = principal amount (initial amount)

r = annual rate of interest (as a decimal) Assumption: Number of decimals used for calculation will be the same as that specified by HO.

A = amount of money accumulated including interest

n = number of times the interest is compounded per years

Periodic intervals: daily, monthly, quarterly, semiannually, or annually (This can be number of days and number of weeks too.)

EMI Definition: EMI (Equated Monthly Installment) is the amount payable to the lending institution every month, till the loan is paid back in full. It consists of a portion of the interest as well as the principal.

Declining Balance Interest (EMI of Principal and Interest)

Declining Balance Definition: Interest is computed at periodic intervals on the amount of the original principal that has not yet been repaid. Since the borrower only pays interest on that amount of original principal that has not yet been repaid, interest paid is smaller every period. However, to make sure that the borrower sets EMI, the formula is:

EMI formula:

EMI = i*P / [1- (1+i)^-n]

Where,

P = Loan amount

r = Rate of interest per year

n = Term of the loan in periods

l = Length of a period (fraction of a year, i.e., 1/12 = 1 month, 14/360 = bi-weekly.)

i = Interest rate per period (r*l)

Examples:

P=1000, r = 5/100, l = 6/12 n = 2, i = 0.025

EMI = 0.025 * 1000 / [1-(1+0.025)^-2]

EMI = $518.83

The way to apply payments is as follows:

            Calculate interest in the principal due: If balance = $1000, and i = 0.025, interest is $25

            Calculate the amount to principal which is the monthly payment minus the interest due: $518.83 - $25 = $493.83

            Calculate the principal remaining, which is the previous principal remaining minus the amount applied to principal: $1000 - $493.83 = $506.17 (remaining balance)

            Once next payment is received, repeat steps 1 to 3.

Note: Due to rounding of computed values, it could potentially be off by a maximum of N number of pennies after the full term of the loan. It will never be short if we round up, rather, principal could end up with a few more pennies. 

Declining Balance Interest – Interest in Periodic Payments; Principal at the End (or Earlier)

Declining Balance Definition: Interest is computed at periodic intervals on the amount of original principal that have not yet been repaid. Since the borrower only pays interest on that amount of original principal that has not yet been repaid, interest paid is smaller every period.

For this interest type, the client only needs to pay per period the interest and the complete principal at the end of the loan cycle. Thus, per period the client pays the same interest amount, unless he or she pays part of the principal ahead. If so, the future periodic payments are less the interest amount.

Note:

            Early payments of principal/interest will not be handled in version 1.0.

            If loan is disbursed in between two meetings, interest installments are not EMIs.

Formula:

For one period interest calculation: interest = P * (r/n)

Where,

P = loan amount- Use the Principal Remaining (which at one point is equal to the initial amount).

r = rate of interest (annual/100)

n = term of the loan

Examples:

P=1000, r = 3% monthly, n = 4

Interest = 1000 *(3/100) = 30

Monthly payments of 30

If client pays 300 of principal, then next payment will be of:

Interest = 700 *(3/100) = 21

Flat Interest

Definition: Flat interest refers to charging interest on the full original loan amount, rather than on the declining balance. For example, with group based loans, a common "interest rate" is "3% per month, flat, for four months". This means that a $100 principal amount lent is multiplied by 3%, and then by 4 months to come up with $12 in interest. Thus, $112 would be repaid over four months in equal installments.

This is the most common calculation used in Grameen Style MFIs (most MFIs). Also there is no incentive for repaying early, since customer still has to pay the total interest as was calculated at the start of the loan.

The use of "flat" interest rates is usually explained as facilitating understanding by poorly educated and illiterate clients. "Flat" interest is easier to calculate than “declining balance” interest. However, "flat" interest also disguises the "effective" interest rate (APR, or internal rate of return) to the loan. Based on how often the principal is collected (weekly, monthly or at the end of the term), and assuming there are no additional fees, the above loan has an APR of between 39% and 71%.

Formula:  Interest = P * r/100 * n

P = loan amount- Initial amount

r = rate of interest

n = term of the loan

Examples:

P=100, r = 3/100 per month, n = 4

Interest = 100 *(3/100) * 4 = 12

Monthly payments of 112 / 4 = 28

Note: The above formula holds for loans disbursed in between two meetings also.

Declining balance interest calculation with equal principal installment

This feature allows MFIs to calculate interest using equal principal installments, and simple declining balance formula to calculate the interest. This means that the borrower pays equal installments of principal for the duration of the loan, and the interest is calculated on principal that has not been paid for the loan period.

Formula Interest = (P-Pp) * r * n

Where,

P = loan amount

Pp= Principal paid

r = rate of interest

n = term of loan

The following example illustrates this:

Principal = 15,000

Int. Rate = 25 %

No of payments = 25

Payment schedule (Every 2 weeks) = 14 days

Principal = 15,000/25 = 600

The following additional logic is needed in the Loan Repayment and Interest Calculation:

1. Calculate the Principal per Installment
   • PPI = Total Principal/ No of Payments
2. Interest Per Period = (P-Pp) * r * n Where, P = loan amount Pp= Principal paid r = rate of interest n = term of loan

Declining balance calculation with interest recalculation

This takes the Declining Balance interest rate type,  but interest charged is updated based on early or late payments.  See Declining Balance - Interest Recalculation FS for more information.