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You have a credit card with a​ 14% APR, compounded​ monthly, and a​ $18,000 balance. You...

You have a credit card with a​ 14% APR, compounded​ monthly, and a​ $18,000 balance. You plan to pay off the entire balance by making quarterly payments for 9 years. a. What is the effective quarterly interest​ rate? b. How much do you pay per​ quarter? c. Over the 9​ years, how much total interest have you​ paid?

a. What is the effective quarterly interest​ rate?

b. How much do you pay per​ quarter?

c. Over the 9​ years, how much total interest have you​ paid?

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Answer #1

monthly interest rate = 14%/12 = 1.167%

a) quarterly interest rate = (1 + monthly interest rate)3 -1 = 3.54%

b) quarterly payment = q

time period = 9 x 4 = 36 quarters

18000 = q/(1 + 3.54%) + q/(1 + 3.54%)2 + .... + q/(1 + 3.54%)36

q = $ 892.35

c) Total payment = 892.35 x 36 = $ 32124.6

Interest (total) = 32124.6 - 18000 = $ 14124.6

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