Question

A certificate of deposit earns 0.75% interest every three months. The interest is compounded. What is the value of a $32,000 investment after 5 years?
$32,426.67

$37,157.89

$43,099.36

$57,795.56

Answer 1

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 32000\\ r=rate\to 0.75\%\to \frac{0.75}{100}\to &0.0075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{every 3months, or quarter} \end{array}\to &4\\ t=years\to &5 \end{cases} \\\\\\ A=32000\left(1+\frac{0.0075}{4}\right)^{4\cdot 5}$

Answer 2

Answer:

$ 37,157.89

Step-by-step explanation:

Given,

The initial deposit, P = $ 32,000,

Which earns 0.75% compound interest every three months.

Thus, the rate per three months, r = 0.75 % = 0.0075.

Time = 5 years,

So, the number of periods ( of three months ) in 5 years, n = 20

( 1 year = 12 months ⇒ The number of three month period in 1 year = 4 )

Thus, the amount after 5 years,

$A=P(1+r)^n$

$=32000(1+0.0075)^{20}$

$=\ 37157.8925537$

$\approx \ 37157.89$