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

$76,670.47

Explanation

Compound interest formula

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