Question

Rich is attending a 4-year college. as a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. he knows he has the option of beginning repayment of the loan in 4.5 years. he also knows that during this nonpayment time, interest will accrue at 4.29%. a. how much interest will rich accrue during the 4.5-year nonpayment period?

b. if rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. what will the new principal be when he begins making loan payments?
c. what will his monthly payment be if he decides to defer payments until after the grace period? round to the nearest whole dollar amount.
d. how much interest will he end up paying once he pays off the load?
e. suppose rich got a subsadised loan instead. what would his monthly payment be? round to the nearest whole number.$ f. what will he now pay in interest over the term of his loan?
g. rich made his last monthly interest-only payment on november 1. his next payment is due on december 1. what will be the amount of that interest-only payment? (there are 30 days in november)

Answer 1

Rich will accrue $1,124.73 in interest during the 4.5-year nonpayment period. The new principal when he begins making loan payments will be $9,024.73. His monthly payment if he decides to defer payments until after the grace period will be approximately $82.36. He will end up paying $1,992.72 in interest once he pays off the loan.

Step-by-step explanation:

a. To calculate the interest accrued during the 4.5-year nonpayment period, we can use the formula:

Interest = Principal × Rate × Time

Interest = $7,900 × 0.0429 × 4.5 = $1,124.73

Therefore, Rich will accrue $1,124.73 in interest during the 4.5-year nonpayment period.

b. If Rich decides to make no payments during the 4.5 years and the interest is capitalized, the new principal will be:

New Principal = Principal + Accrued Interest

New Principal = $7,900 + $1,124.73 = $9,024.73

Therefore, the new principal when he begins making loan payments will be $9,024.73.

c. To calculate his monthly payment if he decides to defer payments until after the grace period, we can use a loan amortization formula:

Monthly Payment = (Principal × Rate) / (1 - (1 + Rate)^(-Number of Payments))

Monthly Payment = ($9,024.73 × 0.0429) / (1 - (1 + 0.0429)^(-120))

Monthly Payment ≈ $82.36

Therefore, his monthly payment will be approximately $82.36.

d. To calculate the total interest he will end up paying once he pays off the loan, we can use the formula:

Total Interest = Total Payments - Principal

Total Payments = Monthly Payment × Number of Payments

Total Payments = $82.36 × 120 = $9,892.72

Total Interest = $9,892.72 - $7,900 = $1,992.72

Therefore, he will end up paying $1,992.72 in interest once he pays off the loan.

e. If Rich got a subsidized loan instead, the interest would not accrue during the nonpayment period. Therefore, his monthly payment would be the same as that calculated in part c, which is approximately $82.36.

f. Assuming all other factors remain the same and he makes the calculated monthly payment of approximately $82.36, the total interest he will pay over the term of his loan can be calculated using the formula:

Total Interest = (Monthly Payment × Number of Payments) - Principal

Total Interest = ($82.36 × 120) - $7,900 = $648.21

Therefore, he will now pay $648.21 in interest over the term of his loan.

g. Since he made his last monthly interest-only payment on November 1 and his next payment is due on December 1, the amount of that interest-only payment can be calculated using the formula:

Interest Payment = (Principal × Rate) × (Number of Days / Total Days in the Month)

Interest Payment = ($9,024.73 × 0.0429) × (30 / 30) = $32.74

Therefore, the amount of his next interest-only payment will be $32.74.