1. **State the problem:** Calculate the monthly payment, total amount paid, and interest paid for two types of student loans: a subsidized loan and an unsubsidized loan with simple interest accrued during 4 years in school. 2. **Given data:** - Principal amount $P = 32742$ - APR $r = 7.44\% = 0.0744$ annually - Number of years in school $= 4$ - Number of payments per year $n = 12$ - Loan term after school $t = 10$ years 3. **Formulas:** - Monthly interest rate $i = \frac{r}{n} = \frac{0.0744}{12}$ - Total number of payments $N = n \times t = 12 \times 10 = 120$ - For subsidized loan (no interest accrues during school), monthly payment formula for amortized loan: $$ PMT = P \times \frac{i(1+i)^N}{(1+i)^N - 1} $$ - For unsubsidized loan, interest accrues during school as simple interest: $$ \text{Interest accrued} = P \times r \times 4 $$ New principal after school: $$ P_{new} = P + \text{Interest accrued} $$ Then monthly payment calculated with $P_{new}$ using the same amortized formula. 4. **Calculate monthly interest rate:** $$ i = \frac{0.0744}{12} = 0.0062 $$ 5. **Calculate monthly payment for subsidized loan:** $$ PMT = 32742 \times \frac{0.0062(1+0.0062)^{120}}{(1+0.0062)^{120} - 1} $$ Calculate powers: $$ (1+0.0062)^{120} = (1.0062)^{120} \approx 2.098 $$ Substitute: $$ PMT = 32742 \times \frac{0.0062 \times 2.098}{2.098 - 1} = 32742 \times \frac{0.01301}{1.098} = 32742 \times 0.01184 = 387.77 $$ 6. **Calculate total amount paid and interest for subsidized loan:** $$ \text{Total paid} = PMT \times N = 387.77 \times 120 = 46532.40 $$ $$ \text{Interest paid} = 46532.40 - 32742 = 13790.40 $$ 7. **Calculate interest accrued during school for unsubsidized loan:** $$ \text{Interest accrued} = 32742 \times 0.0744 \times 4 = 9747.56 $$ 8. **New principal for unsubsidized loan:** $$ P_{new} = 32742 + 9747.56 = 42489.56 $$ 9. **Calculate monthly payment for unsubsidized loan:** $$ PMT = 42489.56 \times \frac{0.0062(1.0062)^{120}}{(1.0062)^{120} - 1} = 42489.56 \times 0.01184 = 503.18 $$ 10. **Calculate total amount paid and interest for unsubsidized loan:** $$ \text{Total paid} = 503.18 \times 120 = 60381.60 $$ $$ \text{Interest paid} = 60381.60 - 32742 = 27639.60 $$ **Final answers:** - Subsidized loan monthly payment: $387.77$ - Subsidized loan total paid: $46532.40$ - Subsidized loan interest paid: $13790.40$ - Unsubsidized loan monthly payment: $503.18$ - Unsubsidized loan total paid: $60381.60$ - Unsubsidized loan interest paid: $27639.60