Mandy takes out a ten-year loan of R80 000. She repays the loan by means of equal monthly payments starting four months after the granting of the loan. The interest rate is 12% per annum compounded monthly. Calculate the monthly payments.
Answer (2)
To calculate the monthly payment for Mandy's loan, we'll need to use the formula for the annuity payment. Mandy has taken out a loan for R80,000 with an interest rate of 12% per annum compounded monthly. The loan is to be repaid with equal monthly payments over ten years, but the repayments start after four months.
First, let's break down the important details:
Principal (P) : R80,000
Annual interest rate (r) : 12%
Monthly interest rate (i) : 100 × 12 12 = 0.01 or 1%
Total number of payments (n) : Payments start four months after the loan is taken, spanning over ten years, which is 10 × 12 = 120 payments.
Since the payments start after four months, the number of compounding periods is 124 months.
Monthly Payment Calculation
The formula for the annuity payment M is:
M = 1 − ( 1 + i ) − n P × i
Substituting the values:
M = 1 − ( 1 + 0.01 ) − 120 80000 × 0.01
Calculating further:
M = 1 − ( 1.01 ) − 120 800
( 1.01 ) − 120 ≈ 0.302498
M = 1 − 0.302498 800
M = 0.697502 800
M ≈ 1146.13
Therefore, Mandy's monthly payment is approximately R1,146.13.
Mandy will make monthly payments of approximately R1,146.13 for her loan of R80,000 at a 12% annual interest rate compounded monthly. The loan is to be repaid over a period of ten years, starting four months after the loan was granted. The calculation utilized the annuity payment formula to derive this amount.
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