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. This is what is due at each installment of a loan.
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Declining Balance Interest (EMI of Principal and Interest) |
Declining Balance Interest with equal principal installment |
Flat Interest Rate |
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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 will be smaller every period. |
The exception from the EMI computed in the first column is that interest is calculated using equal principal installments. The client 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. |
Flat interest refers to charging interest on the full original loan amount, rather than on the declining balance. This is the most common calculation used in Grameen Style MFIs (most MFIs). |
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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) |
Formula Interest = (P-Pp) * r * n Where, P = loan amount Pp= Principal paid r = rate of interest n = term of loan |
Interest = P*r*n Where P = loan amount- Initial amount r = rate of interest n = term of the loan |
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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. |
Principal = 15,000 Int. Rate = 25 % No of payments = 25 Payment schedule (Every 2 weeks) = 14 days Principal = 15,000/25 = 600 For Installment 1:
Total due = Principal + Interest = 600 + 143.83 = 743.83 For Installment 2: Interest = (15000-600)*.25*14/365 = 140 Total due = 600 + 140 = 740 Continue calculating for remaining installments |
P=100, r = 3/100 per month, n = 4 Interest = 100 *(3/100) * 4 = 12 Monthly payments of 112 / 4 = 84 |
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