Question

After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly?

$25,377.11

$25,759.92

$26,148.50

$31,752.78

Answer 1

`\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}\to &\$25000\\ r=rate\to 3\%\to (3)/(100)\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &8 \end{cases} \\\\\\ A=25000\left(1+(0.03)/(4)\right)^(4\cdot 8)\implies A=25000(1.0075)^(32)`

Answer 2

Compound interest formula:
F=P(1+i)^n
P=present value (deposit) = 25000
i=interest per period (quarter) = 0.03/4
n=number of periods (quarter) = 8*4=32

So future value
F=25000(1+0.03/4)^32
= 31752.78