Question

Sophie has $40 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much interest will she earn in 3 years? $

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$40\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}`

`A=40\left(1+(0.05)/(1)\right)^(1\cdot 3)\implies A\approx 46.31~\hfill \underset{earned~interest}{\stackrel{46.31~~ - ~~46}{\approx 6.31}}`

Answer 2

$ 6.31

Explanation:

The TOTAL amount in the account in 3 years will be

40 ( 1+.05)^3 = 46.31

subtract the orignal 40 deposit to get the interest =6.31