Mr. Wilson is planning to buy himself a new car in 3.5 years time. He estimates that the car will cost him R138900 and that the trade-in on his old car 3.5 years from now will be R 15 500. Mr. Wilson decides to open a savings account in which he wants to deposit a fixed amount every month so that he will be able to afford the car. What amount should Mr. Wilson be saving monthly if the bank will pay interest of 13.7% per annum compounded monthly on the savings account?
R 2 307.03
R 2 596.81
R 77.28
None of the above
To calculate the monthly savings amount Mr. Wilson should be saving, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years the money is invested or borrowed for
In this case, Mr. Wilson wants to save up R138900 in 3.5 years, with an interest rate of 13.7% compounded monthly. The formula becomes:
138900 = P(1 + 0.137/12)^(12*3.5)
138900 = P(1 + 0.01141666667)^(42)
138900 = P(1.01141666667)^42
Now we solve for P by dividing both sides by (1.01141666667)^42:
P = 138900 / (1.01141666667)^42
P = 138900 / 1.688687198
P = 82188.43
So, Mr. Wilson should save R82188.43 in total over 3.5 years. To find the monthly savings amount, we divide this total amount by the number of months in 3.5 years:
Monthly savings amount = 82188.43 / (3.5 * 12)
Monthly savings amount = 82188.43 / 42
Monthly savings amount = R 1956.11
Therefore, the correct answer is not listed. It should be R1956.11.