Answer:
The correct answer is:
$515.27 (c.)
Explanation:
The type of account described in this question is called a sinking fund account. In this type of account, a compound interest is earned on periodic payments, over a compounding period in years. Mathematically, the future value on this type of account is calculated using the formula shown below:
[tex]FV=PMT\frac{(1+\frac{r}{n} )^{n*t}-1}{\frac{r}{n} }[/tex]
where:
FV = future value
PMT = periodic payments = 100
r = interest rate in decimal = 9% = 0.09
n = number of compounding period per year = monthly = 12
t = compounding period in years = 3 years
[tex]FV=100\frac{(1+\frac{0.09}{12} )^{12*3}-1}{\frac{0.09}{12} }[/tex]
[tex]FV= 100\frac{(1.0075)^{36}-1}{0.0075}[/tex]
[tex]FV= 100(41.1527161) = 4,115.27161[/tex]
Next, we are going to calculate the interest earned on the initial amount by subtracting the total amount deposited from the future value of the total deposits.
Total monthly deposits made = $100 × number of months
Total time of periodic deposits = 3 years = 3 × 12 months = 36 months
Therefore, Total deposits made = 100 × 36 = $3,600
Interest earned = Final value - Total deposits made
= 4,115.27161 - 3600 = $515.27 (c.)
