Many loans are repaid in equal periodic installments. Part of each payment is interest and other part is principal. After you make each payment, your principal
is reduced by the amount of principal repaid. Therefore, the portion of payment that goes toward interest is lower than previous 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.
