Toby just graduated from four years of college. at the beginning of each year, he took out a stafford loan with a principal of $

Question

1 year ago

5

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 please select the best answer from the choices provided a b c d

Mathematics

1 answer:

Mila [183] · Answer 1 · 2023-06-15T04:12:07+03:00

If he starts paying after four years, the worth of the loans by then is b. $31,616.16

This refers to the amount collected from a lender to be repaid after a given time, usually with added interest.

Hence, we can see that:

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 pays them prompty, then the total lifetime cost would be

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