Question

This is for a finance course for beginners im very confused. Thank you!

Anne has difficulty managing her debt. She usually carriess a balance on her credit card, has maxed out her $16,000 line of credit and now finds herself in the position of having to borrow to purchase a car. a)Assume Annes's credit card balance is $3,000. If she doesn't use her card again and only makes the minimum 3% payment every month, how long will it take her to pay off the balance on her card? The interest rate is 22%, compounded daily. (Calculate credit card repayment period) b)Anne's line of credit charges an /APR / of 8%, compounded monthly. She was charged $200 service fee to set everything up. What is the effective annual cost of the line of credit, assuming full draw down on it? (Calculate effective annual cost of the line of credit)

Answer 1

1) Credit card balance (present value) = $3,000

Monthly payment = 3% * 3000 = $90

Interest rate = 22%

Monthly compounded annual interest rates = (1+22%/365)^365-1 = 24.6%

Monthly interest rate = 24.6% / 12 = 2.05%

Using excel formula for number of period for complete repayment of credit card balance of $3,000

Total number of month required =NPER(2.05%,90,-3000,0)

Total number of month required = 56.7 months = 4.72 years

b) Total annual effective cost of line of credit = 9.55%

Line of credit charges = 8%

Monthly compounded annual charges  = (1+8%/12)^12-1 = 8.3%

Service fees paid to set up line of credit = $200

Total size of line of credit = $16,000

Charges paid % of line of credit = 200 / 16,000 = 1.25%

Total annual effective cost of line of credit = 8.3% + 1.25% = 9.55%