A freight company bought computers for R 79,560 on a hire purchase agreement. They paid an initial deposit of 12% of the purchase price. The balance is to be paid off in equal monthly instalments over 5 years. Calculate the monthly instalment if there is an interest rate charged at 14.75% per annum. Also, the seller adds a monthly insurance premium of R 70.
Answer (1)
To calculate the monthly installment for the computers bought on a hire purchase agreement, we can break this down step-by-step:
Calculate the Initial Deposit
The initial deposit is 12% of the purchase price:
Initial Deposit = Purchase Price × 100 12 = 79 , 560 × 100 12 = 9 , 547.20
Determine the Remaining Balance
Subtract the initial deposit from the purchase price:
Remaining Balance = 79 , 560 − 9 , 547.20 = 70 , 012.80
Calculate the Monthly Interest Rate
The annual interest rate is 14.75%, hence the monthly interest rate is:
Monthly Interest Rate = 12 14.75 = 1.2291667% ≈ 0.012291667
Calculate the Monthly Installment without Insurance
The balance is to be paid over 5 years (which is 60 months). The formula for the monthly installment without insurance, considering compound interest, is given by:
A = ( 1 + r ) n − 1 P ⋅ r ⋅ ( 1 + r ) n Where:
A is the installment
P is the loan principal ( 70 , 012.80 )
r is the monthly interest rate (as a decimal)
n is the number of payments (60)
Using this formula:
A = ( 1 + 0.012291667 ) 60 − 1 70 , 012.80 ⋅ 0.012291667 ⋅ ( 1 + 0.012291667 ) 60 ≈ 1 , 650.68
Add the Monthly Insurance Premium
The monthly insurance premium is R 70. Therefore, the total monthly installment is:
Total Monthly Installment = 1 , 650.68 + 70 = 1 , 720.68
Thus, the monthly installment, including the insurance, is approximately R 1,720.68.
