[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]
The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.
This can be achieved using the future value and present value formulas or factors.
We can also use an online finance calculator, as follows:
Future value = $5,000
Investment period = 3 years
Annual compound interest = 5%
N (# of periods) = 3 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $5,000 ($4,531.56 + $468.44)
Results:
PMT = $1,510.52
Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)
Total Interest = $468.44
Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
Learn more about periodic payments at https://brainly.com/question/24244579
