Peggy Sue has $9,000 balance on a credit card today. She is committed to pay it

Question

Peggy Sue has $9,000 balance on a credit card today. She is committed to pay it off. The rate on the card is 18% APR with monthly compounding. a. How many months would it take for Peggy Sue to reduce the balance to zero if she makes no more charges and makes an electronic payment of $250 today and then every month thereafter makes a payment of $450? b. How many months would it take Peggy Sue to reduce the balance to $1,000 if she makes no more charges and makes a payment at the end of every month of $500 (no electronic payment today)? c. If part a of this question is changed to making a payment of $100, (everything else the same) the function yields a #NUM! error. Why is this?

Explanation / Answer

r = 18/12 = 1.5 %

9000 = 250 + 450/(1.015) + 450/1.015)^2 + ....450/(1.015)^n

19.4444 = 1/(1.015) + 1/1.015)^2 + ....1/(1.015)^n

n = 23.2 months

so n= 24 monhts

c) because monthly interest = 9000*1.5/100 = $135 which is more than $100 so interest will go on accumulating

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