Claudius took out an unsubsidized stafford loan at the beginning of his six-year college career. the loan had a principal of $4,850, an interest rate of 6.5% compounded monthly, and a duration of ten years. if claudius started paying off the loan when he graduated, what is his monthly payment? round all dollar values to the nearest cent. a. $71.37 b. $81.25 c. $55.07 d. $76.55

the answer is B, just took the test

$81.25

Step-by-step explanation:

This is an example of a compound interest loan.

The first step is to calculate the value of the loan in 10 years time

Using the compound interest formula below, we can calculate that

A = P x (1+r)ⁿ                   where A = the future value of the loan

                                                    P  = present value

                                                    r   =  annual interest rate

                                                    n = tenor of loan which is time in years

To convert the annual interest rate into a compounded monthly interest, we divide it by 12

A = $4,850 x (1 + 0.065/12)¹⁰

  =  $4850 x (1 + 0.0054167)¹⁰

  =  $4850 x (1.0054167)¹⁰

  =  $4850 x 1.05413804

A= $5,112.5695178 ≅ $5,112.57 (nearest cent) which is the value of the loan in 10 years time.

From the question, Claudius starts repayment after graduation from his 6-year college course, so he has just 4 years left to repay his loan

Hence his month repayment in 4 years would be

$5,112.57 / 48 months = $81.25

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