Question

Toby just graduated from four years of college. At the beginning of each year, he took out a Stafford loan with a principal of $6,125. Each loan had a duration of ten years and an interest rate of 5. 3%, compounded monthly. All of the loans were subsidized. Toby plans to pay off each loan in monthly installments, starting from his graduation. What is the total lifetime cost for Toby to pay off his 4 loans? Round each loan's calculation to the nearest cent. A. $7,904. 04 b. $31,616. 16 c. $10,393. 82 d. $36,490. 25.

Answer 1

The correct option for the total lifetime cost for Toby to pay off his four loans is $31,616.

Computation of present value of the loans:

The given information is:

Principal = $ 6125

Interest rate = 5.3%

$\text{The effective monthly interest rate} (i) =\frac{0.053}{12} \\ \text{The effective monthly interest rate} (i) = 0.0044$

$\text{The effective annual interest rate} (i) = (1 + 0.0044)^{12} -1\\ \text{The effective annual interest rate} (i) = 0.0543$

The present worth of all the loans is:

$P = 6125 + 6125 \times (1 + 0.0543)^{1} + 6125\times (1 + 0.0543)^{2} + 6125 \times(1 + 0.0543)^{3} \\P = 22,671.40$

If he starts paying after four years, the worth of the loans by then is:

$\text{Total lifetime cost} = P \times \text{Effective Annual Interest Rate}\\\text{Total lifetime cost}= 22671.40\times (1 + 0.0543)^{4} = 31,616.16$

Therefore, the correct option is b.

To know more about the effective interest rates and loans worth, refer to the link below:

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