Question

At the time of her grandson's birth, a grandmother deposits $5000 in an account that pays 9.5% compounded monthly. What will be the

value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
?

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 &\$5000\\ r=rate\to 9.5\%\to (9.5)/(100)\dotfill &0.095\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &21 \end{cases}`

`A=5000\left(1+(0.095)/(12)\right)^(12\cdot 21) \implies A=5000\left( (2419)/(2400) \right)^(252)\implies {\large \begin{array}{llll} A \approx 36473.37 \end{array}}`