Answer to Question #197409 in Financial Math for Yoyo

Question

John will save $5000 in 5 years and the bank has promised to give him 8% interest per annum. [compounded] His friend, Lee, has also decided to save the years but the lender to pay him 8% simple interest on the sum A. Calculate how much John will need to put in the bank now to save the $5,000 in 5 year time. B. Why do they get different rate as interest? Explain why. [use effective annual rate (EAR)of interest to answer this question.

Answer 1

(a)$A=P(1+\frac{r}{n})^{nt}$

A=amount

P=principal

r=interest rate

n=number of times payments are made in a year

t=time

$5000=P(1+\frac{0.08}{1})^{5}$

$5000=1.469328077p$

$P=31402.92$

(b)The difference in rates is because simple interest is based on the amount of saving while compound interest is based on principal amount and interest that accumulates on it every period. Simple interest applies annual percentage rate that tells the true cost of borrowing while effective annual rate of interest applies in compound interest. The EAR is the real return on saving account when the effects of compounding over time are taken into account.