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.