Answer :
Answer:
Account balance = $203,131.31
Interest = $38,203.31
Step-by-step explanation:
To determine how much is in the account after 8 years, we can use the Future Value of Annuity formula:
[tex]FV=\dfrac{PMT\left[\left(1+\dfrac{r}{n}\right)^{nt}-1\right]}{\dfrac{r}{n}}[/tex]
where:
- FV = Future value
- PMT = Regular deposit amount
- r = Annual interest rate (decimal form)
- n = number of times interest is compounded per year
- t = time in years
In this case:
- PMT = $1,718
- r = 5.1% = 0.051
- n = 12 (monthly)
- t = 8 years
Substitute the values into the formula and solve for FV:
[tex]FV=\dfrac{1718\left[\left(1+\dfrac{0.051}{12}\right)^{12 \cdot 8}-1\right]}{\dfrac{0.051}{12}}[/tex]
[tex]FV=\dfrac{1718\left[\left(1.00425\right)^{96}-1\right]}{0.00425}[/tex]
[tex]FV=\$203131.31[/tex]
Therefore, the future value of the annuity after 8 years is $203,131.31.
To calculate how much of the balance is interest, subtract the monthly payment (PMT) multiplied by the number of payments (nt) from the future value (FV):
[tex]\textsf{Interest}=FV-PMT \cdot nt \\\\ \textsf{Interest}=203131.31-1718\cdot 12 \cdot 8 \\\\ \textsf{Interest}=203131.31-164928 \\\\ \textsf{Interest}=\$38203.31[/tex]
Therefore, the interest earned over the 8 years is $38,203.31.
