Aladdin 将 $20 000 存入一个储蓄账户，该账户按年利率 r% 支付复利。利息每季度结算一次。以下公式表示 n 年年底的投资总额。 总额 = $20 000\left(1+\dfrac{1}{100}\right)^{20}$ 求 r 和 n 的值。 答：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
$n=5.$