Carlos took seven years to pay off his loan by making identical quarterly payments. The loan had a principal of $22,375 and 5.49% interest, compounded quarterly. Carlos paid a total of $28,821.67. How much did Carlos pay in service charges

$1,721.274

Explanation:

The amount paid as service charge is the difference between the total amount paid by Carlos on the loan and the total installment due.

Service charge = Amount paid -  Total installment payment

The quarterly installment payment from the loan can be determined as follows:

Quarterly equal installment = Loan amount/Annuity factor

Quarterly interest rate = 5.49%/4 =1.3725%

Annuity factor = 1- (1+r)^(-n)/r

r =1.3725%,

n = 4×7   there are four quarters in a year

Annuity factor = (1- (1.013725)^(-4×7) )/0.01327)

                     = 23.1177

Quarterly installment payment interest

                              = 22,375/23.1177

                            = 967.87

Total amount paid in installment

                             = 967.871× 7 × 4

                               = 27,100.39518

Service charge = Amount paid -  Total installment payment

                         $28,821.67 - 27,100.395

                       =$1721.274

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