Question

Max borrows $19,500 for her last 2 years of college, acquiring a federal student loan at 7.1% interest. For a 10 year loan, find the following if she acquires the loan in August, graduates 2 years later, and payments begin 3 months later: a. Find the monthly payment after graduation if interest is not capitalized. b. Find the full monthly payment after graduation if interest is capitalized. c. How much money would be saved by not capitalizing interest.

Answer 1

To find the monthly payment after graduation if interest is not capitalized for a 10 year loan, use the loan payment formula. To find the full monthly payment after graduation if interest is capitalized, calculate the grace period interest and add it to the loan amount. To calculate the money saved by not capitalizing interest, subtract the full monthly payment from the monthly payment if interest is not capitalized and multiply by the total number of payments.

Step-by-step explanation:

a. To find the monthly payment after graduation if interest is not capitalized, we can use the formula for calculating the monthly payment for a loan. The formula is:Monthly payment = (Loan amount * (Interest rate/12) * (1 + (Interest rate/12))^Total number of payments) / ((1 + (Interest rate/12))^Total number of payments - 1)In this case, the loan amount is $19,500, the interest rate is 7.1%, and the total number of payments is 10 years * 12 months/year = 120. Plugging in these values, we can calculate the monthly payment.

b. To find the full monthly payment after graduation if interest is capitalized, we need to calculate the interest that accrues during the 3-month grace period and add it to the loan amount. The interest accrued during the grace period can be calculated using the formula:Grace period interest = Loan amount * (Interest rate/12) * Grace period in months

Adding the grace period interest to the loan amount, we can use the same formula in part a) to calculate the full monthly payment.c. To find how much money would be saved by not capitalizing interest, we subtract the monthly payment in part b) from the monthly payment in part a) and multiply it by the total number of payments.

Answer 2

Max's monthly payment after graduation is $214.22 without capitalized interest and $231.66 with capitalized interest. By not capitalizing interest, she saves $4,119.60 over the loan's 10-year term.

a. $214.22

b. $231.66

c. $4,119.60

Step-by-step explanation:

Max's monthly payment after graduation, without capitalized interest, is $214.22. However, with capitalized interest, the full monthly payment becomes $231.66. By not capitalizing interest, Max saves $4,119.60 over the life of the loan.

When interest is not capitalized, it means that interest does not accrue on the unpaid interest during the in-school and grace periods. The monthly payment is then calculated based on the initial loan amount and the accrued interest. In Max's case, this results in a lower monthly payment of $214.22.

On the other hand, capitalizing interest involves adding the accrued interest to the principal balance at the end of the grace period. This increases the total amount on which future interest is calculated, leading to a higher monthly payment of $231.66.

The $4,119.60 savings by not capitalizing interest is derived from the lower total amount on which interest accrues over the life of the loan. This is a significant financial benefit for Max, as it reduces her overall repayment burden.