Respuesta :
[tex]\bf \qquad \qquad \textit{Future Value of an ordinary annuity}
\\\\
A=d\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]
\\\\\\
\qquad
\begin{cases}
A=
\begin{array}{llll}
\textit{compounded amount}
\end{array}
\begin{array}{llll}
\end{array}\\
d=\textit{periodic deposits}\to &50\\
r=rate\to 4.8\%\to \frac{4.8}{100}\to &0.048\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus 12}
\end{array}\to &12\\
t=years\to &10
\end{cases}[/tex]
Answer:
$80.73.
Step-by-step explanation:
We have been given that you invest $50 a month in an annuity that earns 4.8% APR compounded monthly. We are asked to find the amount of money in account after 10 years.
We will compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us convert our given interest rate in decimal form.
[tex]4.8\%=\frac{4.8}{100}=0.048[/tex]
Upon substituting our given values in above formula we will get,
[tex]A=\$50(1+\frac{0.048}{12})^{12*10}[/tex]
[tex]A=\$50(1+0.004)^{120}[/tex]
[tex]A=\$50(1.004)^{120}[/tex]
[tex]A=\$50*1.6145278360416045[/tex]
[tex]A=\$80.726391\approx \$80.73[/tex]
Therefore, we will have $80.73 in the account after 10 years.
