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

Would appreciate if you could show the work for how this is done.

p. s. I later submitted this question and the answer is B.

Question

Tobias Patton

Mathematics

24 March, 13:07

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

Would appreciate if you could show the work for how this is done.

p. s. I later submitted this question and the answer is B.

+5

Answers (1)

Know the Answer?

Octavio Cabrera · Answer 1

The effective monthly interest rate is:

i = 0.053/12 = 0.0044

The effective annual interest rate is:

i = (1 + 0.0044) ^12 - 1 = 0.0543

The present worth of all the loans is:

P = 6125 + 6125 (1 + 0.0543) ^-1 + 6125 (1 + 0.0543) ^-2 + 6125 (1 + 0.0543) ^-3

P = $22,671.40

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

P = 22671.40 (1 + 0.0543) ^4 = 31,616.16