Thom owes $7,200 on his credit card. The credit card carries an APR of 18.4 percent compounded monthly. If Thom makes monthly payments of $225 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges

45 months

Explanation:

Credit owed $7200

Monthly payment $225

APR annaully 18.4%

Monthly APR = 18.4/12 = 1.533%

SOLUTION

1st Month interest payment

1.533% x $7200 / 100 = $110.40

Principal paid (monthly payment - interest paid) = $225 - $110.40 = $114.60

Balance ( principal - principal paid) = 7200 - 114.60 = $7085.40

2nd Month interest payment

1.533% x $7085.40 / 100 = $108.64

Principal paid (monthly payment - interest paid) = $225 - $108.64 = $116.36

Balance ( principal - principal paid) = $7085.40 - $116.36 = $6969.04

By following this step up to the 45th month you get $74.74 as the monthly payment this sums up to.

Month interest payment

1.533% x $74.74 / 100 = $1.15

Principal paid (monthly payment - interest paid) = $75.88 - $1.15 = $74.74

Balance ( principal - principal paid) = $74.74 - $74.74 = $0

The payment would be completed at exactly 45months

the third answer is correct.

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