Questions: Format all financial amounts as Currency with the symbol and 2 decimal places, and all n and t entries as Number with 0 decimals. Subsidized Student Loan (determine the Unsubsidized Student Loan (determine the monthly payment required for a 10-year loan) monthly payment required for a 10-year loan that accrues simple interest while in school for 4

Solution Steps

To find the monthly payment for the subsidized student loan, we use the formula for the monthly payment \( M \) of an amortizing loan:

\[ M = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1} \]

where:

• \( P = 10000 \) (principal amount)
• \( r = \frac{5}{100 \cdot 12} \) (monthly interest rate)
• \( n = 10 \cdot 12 \) (total number of payments)

Substituting the values, we calculate \( M \).

For the unsubsidized loan, we first calculate the simple interest accrued during the 4 years in school using the formula:

\[ \text{Simple Interest} = P \cdot r \cdot t \]

where:

• \( P = 10000 \) (principal amount)
• \( r = \frac{5}{100} \) (annual interest rate)
• \( t = 4 \) (time in years)

This gives us the total interest accrued, which we then add to the principal to find the new principal amount.

Using the new principal amount from Step 2, we again apply the monthly payment formula:

\[ M = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1} \]

where:

• \( P = 12000 \) (new principal amount after adding simple interest)
• \( r = \frac{5}{100 \cdot 12} \) (monthly interest rate)
• \( n = 10 \cdot 12 \) (total number of payments)

Substituting these values, we calculate the monthly payment \( M \) for the unsubsidized loan.

Final Answer