Aladdin invested $20 000 in a savings account which pays compound interest at the rate of r% per year. The interest is compounded quarterly. The formula below shows the total amount of the investment at the end of n years. Total amount = $20 000\left(1+\dfrac{1}{100}\right)^{20}$ Find the value of r and n. Ans: r = ___ n = ___

1. Write the standard formula for compound interest compounded quarterly and match the periodic interest rate.

For interest rate $r\%$ per year compounded quarterly,
$\text{Amount}=20000\left(1+\frac{r}{4\times100}\right)^{4n}=20000\left(1+\frac{r}{400}\right)^{4n}.$
Comparing with
$20000\left(1+\frac{1}{100}\right)^{20},$
$\frac{r}{400}=\frac{1}{100}.$

2. Find the annual rate and the number of years by comparing the exponent.

$r=400\times\frac{1}{100}=4.$
Also,
$4n=20,$
so
$n=5.$