Ruben wants to buy a car for a price of 285 000 South African rand (ZAR). He goes to a bank to get a loan to buy the car. To be eligible for the loan, Ruben must make an initial down payment equal to 25% of the price of the car.

The bank offers him a 5-year loan for the remaining balance, with a 4.5% nominal interest rate per annum, compounded monthly. Ruben will pay the loan in fixed payments at the end of each month.

(a) (i) Find the original amount of the loan after the down payment is paid. Give the exact answer.
(ii) Calculate Ruben’s monthly payment for this loan, to two decimal places. [5]

(b) Using your answer from part (a)(ii), calculate the total amount Ruben will pay over the life of the loan, to the nearest ZAR. Do **not** include the initial down payment. [2]

Ruben would like to repay the loan faster and increases his payments such that he pays 4600 ZAR each month.

(c) Find the total number of monthly payments he will need to make to pay off the loan. [2]

This strategy will result in Ruben’s final payment being less than 4600 ZAR.

(d) Determine the amount of Ruben’s final payment, to two decimal places. [4]

(e) Hence, determine the total amount Ruben will save, to the nearest ZAR, by making the higher monthly payments. [3]