Douglas has a credit card with an interest rate of 11.05%, compounded monthly. He used his credit card to buy a new sofa, which cost $670 before the sales tax of 7.94%. Douglas paid off his balance by making equal monthly payments for three years. Assuming that he had no other purchases on his credit card, how much did Douglas pay in total for the sofa? (Round all dollar values to the nearest cent.)

a. $1,005.93

b. $790.20

c. $723.20

d. $852.84

Question

Mathematics

Asa Schultz

22 May, 03:27

Douglas has a credit card with an interest rate of 11.05%, compounded monthly. He used his credit card to buy a new sofa, which cost $670 before the sales tax of 7.94%. Douglas paid off his balance by making equal monthly payments for three years. Assuming that he had no other purchases on his credit card, how much did Douglas pay in total for the sofa? (Round all dollar values to the nearest cent.)

a. $1,005.93

b. $790.20

c. $723.20

d. $852.84

+4

Answers (1)

Know the Answer?

Leila Watkins · Answer 1

This problem can be solved using the formula for the annuity.

Principal amount = price of the sofa (1 + sales tax)

where

price of the sofa = $670

sales tax = 7.94%

Principal amount = $723.2

solve for the amortization using the formula:

Amortization = Principal amount[ (i (1+i) ^n]/[ (1+i) ^n-1]

where

i = 11.05%/12=.92%

n = 3years x 4 payments/year=36

Principal amount = $723.20

Amortization = $23.68

Get the sum of annuity

Sum of annuity=Amortization[ (1+i) ^n-1]/i

Sum of annuity = $852.84

The answer is letter d. Douglas paid a total of $852.84 for the sofa.