Question

Beverly transferred a balance of $2250 to a new credit card at the beginning of the year. The card offered an introductory APR of 3.6% for the first 3 months and a standard APR of 28.8% for the rest of the year. Beverly made no payments or new purchases during the year, and she wasn't charged any late payment fees. The credit card compounds interest monthly. Help Beverly figure out how much money the introductory APR saved her over the course of the year. (5 points: Part I – 1 point; Part II – 1 point; Part III – 1 point; Part IV – 1 point; Part V – 1 point) Part I: What was Beverly’s balance at the end of the introductory period? Part II: For how many months during the year did Beverly have the standard APR? Part III: What was Beverlys balance at the end of the year? Part IV: What would Beverlys balance have been at the end of the year had there not been an introductory APR? Part V: How much money did the introductory APR save Beverly over the course of the year?

Answer 1

Given:
Initial amount owing, P=2250
APR for first three months, i1=0.036/12=0.003 per month
APR for the remaining 9 months, i2=0.288/12=0.024 per month.

Need:
1. balance at the end of first 3 months
2. number of months at regular APR (i2).
3. balance at the end of the year
4. balance at the end of the year if interest had been at regular APR for all 12 months.
5. How much did she "save".

The question is based on the compound interest formula,
F=P(1+i)^n where
F=future outstanding balance,
P=initial balance
i=interest rate per month
n=number of months.

1. Balance at the end of three months (at special APR)
F1=P(1+i1)^n=2250(1+0.003)^3=2270.31
2. For nine months Beverly paid regular APR of 28.8%
3. Balance at the end of the year
F2=F1(1+i2)^n=2270.31(1+0.024)^9=2810.51
4. Balance at end of year if interest were 28.8% all year round
F3=2250(1+0.024)^12
=2990.76
5. Amount Beverly "saved" = F3-F2=2990.76-2810.51=180.25