Respuesta :
[tex]\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}[/tex]
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,
[tex]A=P(1+r)^n[/tex]
[tex]=32000(1+0.0075)^{20}[/tex]
[tex]=\$ 37157.8925537[/tex]
[tex]\approx \$ 37157.89[/tex]
