In the financial world, amortization is basically the payment of a loan by installment usually monthly such as a home mortgage or a car loan the amount of which is so much that not too many can afford to pay it in just one payment. The monthly payment can be calculated and an amortization schedule or table can be constructed quickly with the aid of Microsoft Excel or the internet at www.bankrate.com provided loan details i.e. loan amount, annual interest rate, loan period in years, and number of payments per year are available. A mathematical formula can also be used in calculating the monthly payment and constructing the amortization table.The formula is n n
Payment=PV x i(1+i) / (1+i)-1
where i=interest rate per payment period
n=number of payments
PV=principal amount of the loan
The application of the formula can be daunting because not all of the numbers given in the loan details can be directly substituted in the formula and it requires some basic understanding of the use of a calculator. After calculating the monthly or periodic payment, the interest and payment-to-principal for each payment must be determined. The interest at the end of the first payment period is equal to the interest rate per payment period times the beginning balance or principal amount of the loan. The difference between the payment and the interest is payment-to-principal. The procedure is repeated in each payment period with the interest calculated on a declining balance. The important and useful values determined or calculated in each payment period are tabulated to form an amortization schedule.
As an exercise calculate the monthly payment in the amortization of a loan with the following loan details.
Loan amount $22,499.00 PV = 22,499.00
Annual interest rate 3.99% i = 0.0399/12 or 0.003325
Loan period in years 2 n = 2 x 12 or 24
No. of payments per year 12
24 24
Solution: 1. Monthly Payment = 22,499.00×0.003325 (1.003325) / (1.003325) – 1
= 976.91687 or $ 976.92
2. Interest = 22,499.00×0.003325
= 74.809175 or $74.81 for 1st payment period
3. Principal = 976.92 74.81
= $902.11 payment-to-principal for 1st payment period
4. Balance = 22,499.00 902.11
= $21,596.89 beginning balance for the 2nd payment period
Repeat steps 2-4 for each payment period with the interest calculated on a declining balance and tabulating all relevant values for an amortization schedule. It is important to note that results of the calculations are rounded to two decimal places and will require a little adjustment of the payment amount of the last payment period. If you continue with the exercise you will find that the last payment will come out as $973.68 instead of the monthly payment calculated as $976.92. TEXAS INSTRUMENTS TI-3511 is the calculator used in this exercise.