Question

Luke took out a 10-year Federal Direct Unsubsidized loan for $ 15,000 with a 4.29% APR. If he makes no payments during the first 4.5 years, what will the new loan amount be?

Answer 1

To calculate the new loan amount after 4.5 years of no payments on a $15,000 Federal Direct Unsubsidized Loan with a 4.29% APR, the compound interest formula is used assuming the interest compounds annually. The formula to apply is
`P(1 + r/n)^(nt)`, yielding the increased new loan amount due to accrued interest.

Luke took out a 10-year Federal Direct Unsubsidized Loan for $15,000 with an annual percentage rate (APR) of 4.29%. To find out what the new loan amount will be after 4.5 years with no payments made, we need to calculate the compound interest on the loan during this period.

The general formula for compound interest is
`P(1 + r/n)^(nt)`, where:

• P is the principal amount (the initial loan amount).
• r is the annual interest rate (in decimal form).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

Assuming that the interest compounds annually (which is typical for student loans unless otherwise specified), we use n = 1. Thus, we calculate the new amount as follows:

New Loan Amount = 15000(1 + 0.0429)^4.5

After calculating this, we can determine that the new loan amount after 4.5 years will be higher than the initial loan due to accrued interest.