Answer to Question #322502 in Financial Math for Busi

Question

Round the answer to this question to the nearest rand. David borrowed R911 012,00 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 R682 081,77. With the

new interest rate, his monthly payments will increase by

[1] R12 745,00

[2] R7 705,00

[3] R3 649,00

[4] R558,00

Answer 1

Periodic payments, given the present value is found as:

$Pmt=\frac{PV}{[\frac{1-(1+\frac{r}{m})^{-(mn)}}{\frac{r}{m}}]}$

If the present value of the loan is R911012 to be repaid after 12 years with an interest rate of 12.4% , then the initial monthly payments will be

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

$Pmt=R12187$

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

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

$Pmt=R12745$

David's monthly payments increases by R558, i.e. $(R12745-R12187)$ .