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Amortization and Sinking Funds

i) Amortization If a loan is repaid on installment (usually in equal amounts), then the loan is said to be repaid by the amortization method. Under this method, each installment includes the repayment of principal and the payment of interest. The payments form an annuity whose present value is equal to the original loan.

1) Finding the periodic payment: Example 1: A debt of 12,500 with interest at 8%, compounded quarterly, is to be amortized by equal payments at the end of each 3 months for 5 years. Find the size of the quarterly payment.

Example 3: A 22,000 debt is to be amortized in 15 payments every 6 months. Find the semi-annual payment and the outstanding balance after the 7th payment. Money is worth 13% converted semi-annually.

Example 4. Allan borrows 30,000 at 9% effective interest. The debt is to be repaid annually in 18 years. Find the outstanding principal after the 10th payment.

Example 5: A 7,500 loan is amortized annually at 800. The interest is 10% effective. Find the outstanding principal after the 5th payment. (Note: The prospective method cannot be applied in this problem.)

Example 6: A loan is amortized annually at 1,800. If the outstanding principal in 4 years is 10,000, find the original loan.

Amortization Schedule:

The outstanding principal at the end of the first period is equal to the difference between the outstanding principal at the beginning of the first period and the principal repaid. That is, 1,659.087 =2000 -340.913 The rest of the entries can be constructed by repeating the procedure.Assignment:

Page: 95Items: 1 and 10Book: Mathematics of Investment by Victoria C. Naval, et.,al.Topic: Amortization

c) Sinking Fund Schedule

Note that the amount in the fund after 6 periods equals the total interest plus the total sinking fund deposit.

Example 3: In order to have 8,000 in 5 years, a man deposits each year in a sinking fund earning 6% effective. Find the annual deposit and construct a sinking fund schedule.

Example 4: To pay for plant expansion, a factory manager estimates that 25,000 will be needed in 6.5 years. He decides that the factory should invest a sum every 3 months in a fund. Interest is earned at 12% converted quarterly.a) How much is the quarterly investment?b) How much will be in the fund after the 10th deposit?c) How much interest is earned on the 8th deposits date?d) How much will the fund increase be on the 10th deposit date?