Kayla has a balance of $1479 on her credit card. Since she is unable to pay off the balance in full at the end of the month, the credit card company will charge her 2% interest per month on the outstanding balance at the end of each month. She plans on paying $X each month until the card is paid off in full.
1. Write a recursive rule for Kayla's credit card balance a_n, after the credit card company charges her the monthly interest.
2. To the nearest dollar, find value of X that will hold the card balance steady at $1479, after interest.
3.Kayla is considering whether to pay the card off at a rate of $65 per month or $130 per month. For each monthly payment, find the number of months required to pay the card off in full, and the total amount paid.
A recursive rule is generally used for Arithmetic and Geometric series. Here I will use a Time Value of Money(TVM) formula which does the same thing in this case.
1) FV = PV [1 + i ]^n, where FV=future value, PV=present value, i=interest rate per period(as a decimal), n=number of periods.
FV = 1,479 [1 + 0.02 ]^1
FV = 1,479 x 1.02
FV =$ 1,508.58 This is the balance of Kayla's credit card after 1 month's interest was charged.
2) To hold her balance steady, Kayla must pay $29.58 or about $30 per month, which the interest only @ 2% on $1,479 credit card balance.
3) On this question, I will give you only the answers and the formula to calculate them. It is up to you to verify the answers I give you:
If she pays $65 per month, it will take her 30.66 months to pay the entire credit card balance off.
If she pays $130 per month, it will take her 13.04 months to pay the entire credit card balance off.
The formula used to calculate these results is:
PV=P{[1 + i]^n - 1.[1 + i]^-n} r^-1
1,479 =65 x {[ 1.02^n - 1 ] x 1.02^-n x 0.02^-1}, solve for n.
Hint: You have to use logs to solve for n.
Thanks for your reply. But in this case, I need a recrusive rule. What would it be?
You can go online and read about it here. If your teacher hasn't taught you what a "recursive rule" is, then he or she shouldn't use it in a question such as this one. It doesn't belong here. There are other "rules" or "formula" in financial situations better suited for this question than the "recursive rule." Anyway, read about here and if you don't understand it, talk to your teacher:
http://mathbitsnotebook.com/Algebra1/Functions/FNSequenceFunctionsRecursive.html
