Beginning in January, a person plans to deposit $100 at the end of each month into an account earning 9% compounded monthly. Each year taxes must be paid on the interest earned during that year. Find the interest earned during each year for the first 3 years. a.$899.01b.$694.58c.$515.27d.$506.7 3

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:

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

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.)

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