Answer to Question #128760 in Financial Math for Phenyo

Question

Johan wants to buy a car for R550 000. He must pay a 10% deposit and take out a loan for the remaining amount. The interest rate on the loan is 8% pa compounded monthly over a period of 7 years.
2.1.1 Calculate the value of the deposit. (1)
2.1.2 Calculate his monthly payment. (5)
2.1.3 Johan thinks the loan will have an annual effective interest rate of 8,3%. Is Johan correct? Motivate your answer.

Answer 1

2.1.1)   Deposit= 10/100×550 000

                           =R 55000

2.1.2   Amount=P (1+r/m)^mt            where p=R 550 000-R 55 000=495000           r=8%=0.08, t=7 years is the period taken and m is the monthly payment

               A=495 000(1+0.08/12)^12×7

                 =495 000(1.066)⁸⁴

                  =R 86 4973.90

Monthly repayment =R 864973.90 divided by 84 months

                                     =86 4973.90÷84

                                      =R 10 297

2.1.3   A=495 000(1+8.3/100)⁷

                 =495 000(1.083)⁷

                  =R 86 4976.70

          Joan is correct, because the annual amount interest is equivalent to the monthly interest.

         R 86 4973.90 monthly amount at the rate of 8% and R 86 4976.70 annually amount at the rate of 8.3%