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.

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 6000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &21 \end{cases} \\\\\\ A=6000\left(1+\frac{0.09}{12}\right)^{12\cdot 21}\implies A=6000(1.0075)^{252}\implies A\approx 39437.11$