Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Number 27, 28, and 29! Kayla has a balance of $1479 on her credit card. Since sh

ID: 2783615 • Letter: N

Question

Number 27, 28, and 29!

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 SX each month until the card is paid off in full. 27. Write a recursive rule for Kayla's credit card balance a, , after the credit card company charges her the monthly interest. 28. To the nearest dollar, find the value of X that will hold the card balance steady at $1479 after interest. 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. (Hint: you may wish to use your calculator or a spreadsheet program.) 29. Monthy Months to Total Paid Payment Pay Off $65 $130

Explanation / Answer

Answer 27)

A recursive rule is generally used for Arithmetic and Geometric series. Here A Time Value of Money(TVM) formula can be used 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.

Answer 28

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.

Answer 29)

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}