Question

Zandile is about to purchase a car for R191 810,00 on terms from a car dealer. The terms
are R23 235 deposit and the rest paid in equal quarterly payments of R13 292,48 at the end
of each quarter for four years. The interest rate is 11,5% per year, compounded quarterly.
Considering the amortisation schedule, the principal repaid during the third quarter of the
first year,

Answer 1

The future value (FV) of an investment of present value (PV) amount earning interest at an annual rate of r compounded m times per year for a period of t years is:

                                FV = PV(1 + r/m)^mt

                                            or

                                FV = PV(1 + i)^n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods

thus,

 we have present value (PV) here - 23235

i = 11.5

m=4

nm or we can say n = 16

putting the values in above equation we can get the future value investment.

                              FV=Pv(1+ $\frac{i}{m}$)^mn  

​                               = 23235 x (1 + $\frac{11.5}{4}$) ^16

                                    = 23235 x (1.02875) ^16

                                    = 36567.92

so,                                         36567.92/16

            the principal repaid during the third quarter of the  first year,  

                                    = 2285.49