Loan Amortization

Loan Amortization

Many loans, such as mortgage laons are repaid in equal periodic installments. Part of each payment is interest on outstanding balance and the other part is payment of the principal amount. After each payment, the outstanding balance is reduced by the amount of the principal paid. Therefore, the portion of interest is lower each period as the principal decrease with each period's payment.

For example, let's assume that you take a loan on $100,000 at an interest rate of 10% per year, repaid in 3 annual installments. First, we will calculate the annual payment by finding the PMT that has PV of $100,000 when discounted at 10% for 3 years;
PMT = -((PV(1+i)^n+FV)i)/(1-(1+i)^n)
PMT = -((-100,000(1.10)^3+0) X 0.10) / (1-(1.10)^3)
PMT = $40,211.48

This is the payment that needs to be paid in first year. How much of it is the interest and how much is the principal? Because, the interest rate is 10%, the interest portion of the first payment must be 10% X $100,000 or $10,000. The remainder of $40,211.48 or $30,211.48 is the payment of the original $100,000 of the principal amount. The remaining balance after the first payment is, therefore, $100,000-$30,211.48=$69,788.52. In the second year, how much of the $40,211.48 is interest and how much is the principal? We are left with $69,788.52. Because, the interest rate is 10%, the interest portion of the first payment must be 10% X $69,788.52 or $6,978.85. The remainder of $40,211.48 or $33,232.63 is the payment of the $69,788.52 of the principal amount left. The remaining balance after the second payment is, therefore, $69,788.52-$33,232.63=$36,555.89. The third and final year covers both the interest and the principal on this remaining $36,555.89.