Question

You deposit $175 in an account that pays 4% interest compounded quarterly. How much will you have in the account after 2 years?

A. $182.11
B. $189.50
C. $204.73
D. $239.50

Answer 1

The answer would be d 239.50

Answer 2

`\bf ~~~~~~ \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 &\$175\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}`

`\bf A=175\left(1+(0.04)/(4)\right)^(4\cdot 2)\implies A=175(1.01)^8\implies A\approx 189.50`