Answer to Question #311081 in Financial Math for tumi

Question

Three years ago Lilly borrowed R10 000 from Faith on condition that she should pay her back two years from now. She also owes Faith R6 000 payable five years from now. The applicable interest rate for both transactions is 13,75% per year, compounded every six months. After considering her payback schedule, Lilly asks Faith if she can pay her R9 000 now and the rest in four years' time. She agrees on condition that the new agreement will run from now and that an interest rate of 16,28% per year, compounded monthly, will be applicable from now. The amount that Lilly will have to pay Faith four years from now is

Answer 1

If Lily borrows R10000 three years ago and to repay in two years time, and also borrows R6000 now, to also repay in 5 years time, then are total borrow is:

R10000+R6000=R16000$=PV$

The amount she was supposed to pay back is given as:

$FV=PV (1+\frac{r}{m})^{nm}$

Where n is 5

m is 2

$FV=R16000(1+\frac{13.75\%}{2})^{2×5}$

$FV=R31108.66$

If she agrees to pay R9000 from the total, her balance is R22108.66

If the new interest rate (r) is 16.28% compounded monthly, m, (12) for four years (no)

She'd have to repay Faith:

$FV=R22108.66(1+\frac{16.28\%}{12})^{12×4}$

$FV=R42215.68$