Question

University Bank pays 5% interest compounded quarterly on regular savings accounts and Rosemont

Savings Bank
pays 5.5% compounded semiannually. Vasily and Oxana Cherchenko had $4,000 to invest
for 4 years. Based on the interest to be earned, which bank offers the better investment?

Answer 1

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

`~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\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 &\$4000\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}`

`A = 4000\left(1+(0.05)/(4)\right)^(4\cdot 4) \implies A=4000(1.0125)^(16)\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill`

`~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\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 &\$4000\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}`

`A = 4000\left(1+(0.055)/(2)\right)^(2\cdot 4) \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}`