Question

Suppose that when your friend was born, your friend's parents deposited $5000 in an account paying 5.7% interest compounded quarterly. What will the account balance be after 19 years?​

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 5.7\%\to (5.7)/(100)\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &19 \end{cases} \\\\\\ A = 5000\left(1+(0.057)/(4)\right)^(4\cdot 19) \implies A=5000(1.01425)^(76)\implies A \approx 14655.18`

Answer 2

$337,807.321.

Explanation:

every year has 4 quarters, so 19 years = 76 quarters, so it compounds 76 times = (1+5.7%)^76. so punch into the calculator 1.057 then the "xy"button, then 76, it'll spit out 67.56146111 number. then hit times 5000. which is $337,807.321. power of compounding. More than a quarter million $$$.