[tex]\bf ~~~~~~ \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}\dotfill &\$5400\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &8 \end{cases}[/tex]
[tex]\bf A=5400\left(1+\frac{0.052}{12}\right)^{12\cdot 8}\implies A=5400(1.004\overline{3})^{96}\implies A\approx 8178.43[/tex]
Based on the interest rate, amount invested, and the period compounded, the amount after 8 years would be $8,178.43.
First convert the rate and number of periods to a monthly basis as this is the period of compounding.
Rate = 5.2% / 12 = 5.2/12%
Period = 8 x 12 = 96 months
The amount will be:
= Amount x ( 1 + rate) ^ number of periods
Solving would give:
= 5,400 x ( 1 + 5.2/12%)⁹⁶
= $8,178.43
In conclusion, the account would have $8,178.43.
Find out more at https://brainly.com/question/16081373.
