Answer to Question #190113 in Financial Math for NN HLONGWANE

Question

You buy a computer directly from the manufacturer for R7332,00 and agree to repay it in equal installment over 3 years at the end of each month, starting one month from now. The interest rate is 10.7% per year, compounded monthly. How much will you pay in total?

Answer 1

$PV=733200,$ No. of months in 3 years $n =12\times 3=36 months$

Interest compounded monthly $i =\dfrac{10.7}{12}=0.891$ % $=0.00891$

Using present value formula-

$PV=PMT(\dfrac{1-(1+i)^{-n}}{i}) \\[9pt]733200=PMT(\dfrac{1-(1+0.00891)^{-36}}{0.00891}\\[9pt]733200=PMT\times 30.7\\[9pt]PMT=\dfrac{733200}{30.7}=23882.73$

Total amount we have to pay $= 23882.73\times 36=R859778.50$