Questions: Huai takes out a 3100 student loan at 6.3% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another 12,100 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.1%. Find the total amount of interest that will accrue until payments begin. Part: 0 / 3 Part 1 of 3 (a) Find the total amount of interest that will accrue for loan 1 (community college). The total amount of interest that will accrue for loan 1 (community college) is T. Round your answer to two decimal places, if necessary.

Solution Steps

To find the total amount of interest that will accrue for loan 1, we need to calculate the simple interest over the period from when the loan was taken out until payments begin. The formula for simple interest is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years. For loan 1, the time period is from the start of the loan until 3 months after graduation.

We have the following values for loan 1:

• Principal amount, \( P = 3100 \)
• Annual interest rate, \( r = 6.3\% = 0.063 \)
• Total time until payments begin, \( t = 4 \text{ years} + \frac{4}{12} \text{ years} + \frac{3}{12} \text{ years} = 4.5833 \text{ years} \)

Using the formula for simple interest: \[ I = P \times r \times t \] we substitute the values: \[ I = 3100 \times 0.063 \times 4.5833 \] Calculating this gives: \[ I \approx 895.125 \]

Rounding the total interest to two decimal places, we find: \[ I \approx 895.12 \]

Final Answer