Question

You invest $7000 in an account bearing 5% for ten years. How much will the account be worth if compounded quarterly? What about monthly?

Answer 1

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \qquad \begin{cases} A=\textit{current amount}\\ P=\textit{original amount deposited}\to &\ 7000\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, means 4 times} \end{array}\to &4\\ t=years\to &10 \end{cases}$

how about monthly?  well, there are 12 months in a year, so it will the compound cycle is 12, thus $\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \qquad \begin{cases} A=\textit{current amount}\\ P=\textit{original amount deposited}\to &\ 7000\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, 12 months, thus} \end{array}\to &12\\ t=years\to &10 \end{cases}$

Answer 2

Quarterly
A=5,000×(1+0.05÷4)^(4×10)
A=8,218.097
Monthly
A=5,000×(1+0.05÷12)^(12×10)
A=8,235.047