Final answer:
Calculating the total interest for Rhett's loan involves finding the interest accrued during his college years (4.5 years), which is $2,160, and then adding that to the original principal to get a new principal of $9,660. Over a 10-year period post-graduation, the interest on this new principal totals $6,182.40. Therefore, Rhett will pay a grand total interest of $8,342.40.
Step-by-step explanation:
Let's calculate the total amount of interest Rhett would pay on a 10-year $7,500 Federal Direct Unsubsidized Loan with a 6.4% interest rate, with interest capitalization after graduation.
Calculating the Accrued Interest During College
Firstly, we assume Rhett is in a 4-year college program. Since payments are deferred until 6 months after graduation, interest will accrue for 4.5 years before capitalization.
Annual Interest = Principal x Interest Rate
= $7,500 x 0.064
= $480 per year
Total Accrued Interest after 4.5 years = Annual Interest x 4.5
= $480 x 4.5
= $2,160
Interest Capitalization
Upon capitalization, the accrued interest is added to the principal amount. So the new principal is:
New Principal = Original Principal + Accrued Interest
= $7,500 + $2,160
= $9,660
Calculating Total Interest Paid Over the Loan Term
Using the new principal, we calculate the interest paid over the remaining loan term.
For simplicity, let's assume Rhett pays off the loan in 10 equal annual payments without considering the exact loan amortization schedule.
Annual Interest after capitalization = New Principal x Interest Rate
= $9,660 x 0.064
= $618.24 per year
Total Interest Paid over 10 years = Annual Interest x 10
= $618.24 x 10
= $6,182.40
Grand Total Interest Paid (during college + over the loan term) = Accrued Interest + Total Interest Paid
= $2,160 + $6,182.40
= $8,342.40