Question

How much more would $1000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the interest rate is 3.7%

Answer 1

$\bf ~~~~~~ \textit{Compounding Continuously Interest Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \ 1000\\ r=rate\to 3.7\%\to \frac{3.7}{100}\to &0.037\\ t=years\to &5 \end{cases} \\\\\\ A=1000e^{0.037\cdot 5}\implies A=1000e^{0.185}\\\\ -------------------------------$

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 1000\\ r=rate\to 3.7\%\to \frac{3.7}{100}\to &0.037\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &5 \end{cases} \\\\\\ A=1000\left(1+\frac{0.037}{4}\right)^{4\cdot 5}\implies A=1000(1.00925)^{20}$

compare both amounts.