Answer to Question #318645 in Financial Math for motheo

Question

Round the answer to this question to the nearest rand. David borrowed R911012,00

R911012,00 to refurbish his holiday home. The loan requires monthly repayments over 12 years. When he borrowed the money, the interest rate was 12,4% per annum, compounded monthly, but five years later the bank increased the annual interest rate to 13,9%, in line with market rates. After five years the present value of the loan is R682081,77

R682081,77. With the new interest rate, his monthly payments will increase by

Answer 1

If the present value of the loan is R911012 to be repaid after 12 years with an interest rate of 12.4% but to be changed to a new rate of 13.9% after the fifth year of starting, the monthly payments for the first five years is:$Pmt=\frac{PV}{[\frac{1-(1+\frac{r}{m})^{-(mn)}}{\frac{r}{m}}]}$

$Pmt=\frac{R911012}{[\frac{1-(1+\frac{12.4\%}{12})^{-(12×5)}}{\frac{12.4\%}{12}}]}$

$Pmt=R20450$

After the fifth year, the interest rate changes to 13.9%, the present value becomes R682018.77 and n becomes 7

$\therefore Pmt=\frac{R682081.77}{[\frac{1-(1+\frac{13.9\%}{12})^{-(12×7)}}{\frac{13.9\%}{12}}]}$

$Pmt=R12745$

His monthly payments decreases by R7705 (R20450-R12745).