Answer :
Given:
The time of the investment = 7 years and 3 months = 7 1/4 years
The interest rate = r = 7% = 0.07
compounded monthly, n = 12
We will find the monthly deposit (P) to accumulate $14,500
We will use the following formula:
[tex]A=\frac{P((1+\frac{r}{n})^{nt}-1)}{\frac{r}{n}}[/tex]Substitute: A = 14500, t = 7.25, r = 0.07, n = 12
[tex]\begin{gathered} 14500=P*\frac{((1+\frac{0.07}{12})^{12*7.25}-1)}{\frac{0.07}{12}} \\ \\ 14500=P*112.9175 \\ \\ P=\frac{14500}{112.9175}=128.4122874 \end{gathered}[/tex]Rounding to the nearest tenth
So, the answer will be The monthly deposit = 128.41