Question

This is the question

You invest 6500 in a bank account that has 9% annual interest rate. Calculate what you will have in 30 years

If the interest is compounded annually how much is in the account?

If the interest is compounded monthly how much is in the account?

Answer 1

`~~~~~~ \underset{annually}{\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 &\$6500\\ r=rate\to 9\%\to (9)/(100)\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &30 \end{cases}`

`A=6500\left(1+(0.09)/(1)\right)^(1\cdot 30)\implies A=6500(1.09)^(30)\implies A\approx 86239.91 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \underset{monthly}{\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 &\$6500\\ r=rate\to 9\%\to (9)/(100)\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &30 \end{cases} \\\\\\ A=6500\left(1+(0.09)/(12)\right)^(12\cdot 30)\implies A=6500(1.0075)^(360)\implies A\approx 95748.74`