Question

Cash Flow Diagrams needed and this solved please.

(20 Pts.) 8. An individual expects to receive a loan of "X" amount of money two years from now. He also knows that he will need to repay the loan with equal installment payments in years 4 through 8 of $4000. Compute the amount of money, "X", using an interest rate of 10% per year compounded yearly

Answer 1

n= 4 years but amount is paid in 8 instalments of $4000

This means n = 4*2 =8 amount being paid semi-annually

similarly, i = 10% p.a. or 5% semi anualy

amount of laon is X

X = 4000 (F/A, i%, n) =

4000 + (1+i)" - 1

$X = 4000 * \frac{(1+0.05)^{8}-1}{0.05}$

$X = 4000 * \frac{1.477-1}{0.05}$

0.477 X = 4000* 0,05

X = $38196.44

but this amount of X is recived after two years

so the present value of loan of X amount is

X = 38196.44 * $\frac{1}{(1+i)^{n}}$

X = 38196.44 * $\frac{1}{(1+0.1)^{2}}$

X = 38196.44 * 0.8264

X = $31567.3