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Obviously the larger the balloon, the smaller will be the periodic installment payment for a given loan amount. The amortization schedule may be depicted as shown in Table 2.7.
TABLE 2.7 Amortization with a Balloon Payment
| Year | Payment | Interest | Principal Repayment | Outstanding Principal |
|---|---|---|---|---|
| 0 | 25,000 | |||
| 1 | 3,880.2950 | 2,000.00 | 1,880.30 | 23,119.70 |
| 2 | 3,880.2950 | 1,849.58 | 2,030.72 | 21,088.99 |
| 3 | 3,880.2950 | 1,687.12 | 2,193.18 | 18,895.81 |
| 4 | 3,880.2950 | 1,511.66 | 2,368.63 | 16,527.18 |
| 5 | 3,880.2950 | 1,322.17 | 2,558.12 | 13,969.06 |
| 6 | 3,880.2950 | 1,117.52 | 2,762.77 | 11,206.29 |
| 7 | 3,880.2950 | 896.50 | 2,983.79 | 8,222.50 |
| 8 | 8,880.2950 | 657.80 | 8,222.50 | 0.00 |
THE EQUAL PRINCIPAL REPAYMENT APPROACH
Sometimes a loan may be structured in such a way that the principal is repaid in equal installments. Thus, the principal component of each installment will remain constant; however, as in the case of the amortized loan, the interest component of each payment will steadily decline, on account of the diminishing loan balance. Therefore, the total magnitude of each payment will also decline.
We will illustrate the payment stream for an eight-year loan of $25,000, assuming that the interest rate is 8% per annum (Table 2.8).
TABLE 2.8 Equal Principal Repayment Schedule
| Year | Payment | Interest | Principal Repayment | Outstanding Principal |
|---|---|---|---|---|
| 0 | 25,000 | |||
| 1 | 5,125 | 2,000 | 3,125 | 21,875 |
| 2 | 4,875 | 1,750 | 3.125 | 18,750 |
| 3 | 4,625 | 1,500 | 3,125 | 15,625 |
| 4 | 4,375 | 1,250 | 3,125 | 12,500 |
| 5 | 4,125 | 1,000 | 3,125 | 9,375 |
| 6 | 3,875 | 750 | 3,125 | 6,250 |
| 7 | 3,625 | 500 | 3,125 | 3,125 |
| 8 | 3,375 | 250 | 3,125 | 0.00 |
TYPES OF INTEREST COMPUTATION
Financial institutions employ a variety of techniques to calculate the interest on the loans taken from them by borrowers. Thus the interest rate that is effectively paid by a borrower may be very different from what is being quoted by the lender.1
The Simple Interest Approach
If the lender were to use a simple interest approach, then borrowers need only pay interest for the actual period of time for which they have used the funds. Each time they make a partial repayment of the principal, the interest due will come down for subsequent periods.
EXAMPLE 2.22
Michael has borrowed $8,000 from a bank for a year. The bank charges simple interest at the rate of 10% per annum. If the loan is repaid in one lump sum at the end of the year, the amount payable will be:
This consists of $8,000 by way of principal repayment and an interest payment of $800.
Now let us consider a case
