Question

You have accumulated $65,000 in student loans that average 4% interest. You graduate next month and will be paying off the loans over 20 years. Which of the following is most likely to be your monthly payment assuming you pay interest and a portion of the principal each month?

A) $20
B) $400
C) $8,000
D) None of the above

Answer 1

To find the student loan's monthly payment, we use an amortizing loan formula with the principal amount, monthly interest rate, and number of periods. After calculation, the estimated monthly payment is closest to option B) $400.

Step-by-step explanation:

The question falls under the subject of Mathematics and is likely at the College level, given that it discusses the repayment of student loans post-graduation. To calculate the monthly payment, we can use the formula for an amortizing loan, which takes into account the principal, interest rate (as an annual rate), and the number of periods.

First, convert the annual interest rate to a monthly rate by dividing by 12 months. Then use the formula for a fixed monthly payment on an amortizing loan:

PMT = P[r(1+r)^n] / [(1+r)^n - 1]

Where:

• P = principal amount (the initial amount of the loan)
• r = monthly interest rate (annual rate divided by 12)
• n = total number of payments (or periods)

In this case:

• P = $65,000
• r = 4% per year, or 0.04/12 per month
• n = 20 years, or 20*12 months

Plug these numbers into the formula to calculate the monthly payment. Using a financial calculator or amortization software will give a payment that is more accurate, but it will certainly be closer to option B) $400 than any of the other options provided.