Question

Mary wants to have 8500

to travel to South America when she is
21. She currently has 6439
in a savings account earning 4%
annual compound interest. Mary is 13
now.

Will Mary have enough money for her trip when she is 21
?

Answer 1

well, she's 13 now, and when she'll be 21 that's 8 years later, so

`~~~~~~ \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 &\$6439\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases}`

`A = 6439\left(1+(0.04)/(1)\right)^(1\cdot 8)\implies A=6439(1.04)^8 \implies \stackrel{ \textit{yeap, she will \checkmark} }{A \approx 8812.22}`