Peter takes a loan of R510 000.00


1. Peter takes out a loan of R510 000 to be able to buy a house. He pays back the loan over a period of 20 years, starting one month after he bought the house. Interest is charged at 14%p.a., compounded monthly.

1.1 Determine his monthly payments (correct to the nearest cent).

1.2 How long would it take to repay the loan if he were to pay R10 000 each month? (This is not actually prescribed in the NCS).

2. I need R200 000 to buy the car of my dreams. I have been offered a hire purchase agreement at 12,5% p.a. to be repaid in 48 equal monthly instalments.

2.1 What will be the amount of the monthly repayments?

2.2 Show that a bank loan at 21% p.a. compounded monthly on the reducing balance is a better option.

2.3 What hire purchase rate would be better than the 21% bank loan?

3. A loan of R180 000 is to be repaid over 20 years by means of equal monthly payments, starting one month after the loan is granted. The interest rate is 16% p.a. compounded monthly.

3.1 Calculate the monthly repayments.

3.2 Calculate the outstanding balance after 10 years.

Deferred annuities

In many situations, the repayment of a loan begins one month or one period after the granting of the loan. However, circumstances arise where the repayment of the loan is deferred or delayed for an agreed period of time.

Example

Nthabi borrows R420 000 to start a small business. She agrees to repay the loan over a period of five years, from the time the loan is granted. The first payment, however, will be nine months after the granting of the loan. The interest rate is 18% p.a. compounded quarterly. Calculate the quarterly instalments.

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