Question

In order to pay for college the parents of a child invest $30,000 in a bank that pays 5% interest compounded semi annually how much money will there be in 19 years round your answer to the nearest cent

Answer 1

Answer

$76,670.47

Step-by-step explanation

Compound interest formula

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

where

• A: final amount

,

• P: principal

,

• r: interest rate, as a decimal

,

• n: number of times interest applied per year

,

• t: time in years

Substituting with P = $30,000, r = 0.05 (= 5/100), n = 2 (semi annually means two times per year), and t = 19 years, we get:

$\begin{gathered} A=30000(1+\frac{0.05}{2})^{2\cdot19} \\ A=30,000(1.025)^{38} \\ A=\text{ \ }76,670.47 \end{gathered}$