Question

Calculate the total cost of a 15-year, $20,000 student loan at an interest rate of 4.5% per year compounded monthly. Round to the nearest dollar.

a) $30,000
b) $24,000
c) $17,000
d) $27,000

Answer 1

The total cost of the 15-year, $20,000 student loan at an interest rate of 4.5% per year compounded monthly is approximately $4,969,354.67.

Step-by-step explanation:

To calculate the total cost of a 15-year, $20,000 student loan at an interest rate of 4.5% per year compounded monthly, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)

Where:

• FV = Future value
• P = Principal (initial amount)
• r = Annual interest rate (as a decimal)
• n = Number of compounding periods per year
• t = Number of years

Plugging in the values from the question, we get:

FV = $20,000 * [(1 + 0.045/12)^(12*15) - 1] / (0.045/12)

FV ≈ $20,000 * (1.00375^(180) - 1) / (0.00375)

FV ≈ $20,000 * (1.931726 - 1) / (0.00375)

FV ≈ $20,000 * 0.931726 / 0.00375

FV ≈ $20,000 * 248.4677333

FV ≈ $4,969,354.67

So, the total cost of the loan is approximately $4,969,354.67.