Question

Joffrey deposited $3,000 at 2.6% interest, compounded quarterly, when he was 20 years

old.
How much will be in the account when he is 44 years old if he made no other deposits or
withdrawals?

Answer 1

so, he was 20 at the time of the deposit, so at 44 is just 24 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 &\$3000\\ r=rate\to 2.6\%\to (2.6)/(100)\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &24 \end{cases} \\\\\\ A = 3000\left(1+(0.026)/(4)\right)^(4\cdot 24) \implies A = 3000( 1.0065)^(96)\implies A \approx 5587.84`