Question

A loan of R500 000 is taken out at an interest rate of 9% pa, compounded monthly. It is safe equal monthly payments of R6000 and a final payment less than R6 000. How many payments of R6 000 are needed to pay off the loan?

A. 61 payments
B. 62 payments
C. 63 payments
D. 64 payments

Answer 1

To calculate the number of payments needed to pay off the loan, use the loan formula. In this case, approximately C) 63 payments are needed to pay off the loan.

Step-by-step explanation:

To calculate the number of payments needed to pay off the loan, we can use the loan formula:

Loan = Payment*((1+r)^n - 1)/(r*(1+r)^n)

Where Loan is the initial loan amount, Payment is the monthly payment, r is the monthly interest rate, and n is the number of payments.

In this case, Loan = R500 000, Payment = R6000, and r = 9%/12 = 0.0075.

Substituting these values into the formula, we get:

R500 000 = R6000*((1+0.0075)^n - 1)/(0.0075*(1+0.0075)^n)

Multiplying both sides by 0.0075*(1+0.0075)^n, we get:

3750*(1.0075^n - 1) = (1+0.0075)^n

Now, we can solve this equation for n using either trial and error or a calculator. In this case, the number of payments needed is approximately 63 payments.