Question

a grandmother deposits $6000 in an account that pays 9% 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

now, we're assuming she made the deposit at the child's birth, namely when year was 0, at the child's twenty-first birthday that'll be 21 years later.

`~~~~~~ \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 &\$6000\\ 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 &21 \end{cases} \\\\\\ A=6000\left(1+(0.09)/(12)\right)^(12\cdot 21)\implies A=6000(1.0075)^(252)\implies A\approx 39437.11`