The due date for the balance of $2,000 on your credit card is tomorrow and you h

Question

The due date for the balance of $2,000 on your credit card is tomorrow and you have only enough money to survive the next six months without paying this debt. In six months you will have enough money to pay off the debt. The credit card company charges 18% p.a., compounded monthly. Kneecap Finance offers a better rate, 16%, compounded weekly (assumes 52 weeks in a year). (a) Should you borrow $2,000 from Kneecap to pay the credit card bill? Assume there are 26 weeks in six months. (b) Suppose you were earning enough money each week during the next six months that you could repay a loan in the usual form of blended pay- ments (principal and interest). How much would you pay each week if you borrowed $2,000 for six months from Kneecap? (c) In reality, there is a bit of a problem comparing the two alternatives by assuming there are 26 weeks in six months. You can do it mechanically, but do credit card companies all charge interest on part months?

Explanation / Answer

$ 2000 with the credit card company will become in 6 months at 18% monthly compounding = 2000 * (1+18%/12)6 = $ 2186.89

With kneecap, at 16% weekly compounding, the amount will be = 2000 * (1+16%/52)26 = $ 2166.31

Since the kneecap, repayable in 6 months will be lower, the person should borrow from Kneecap.

(b) We need to find out the weekly payment which will completely pay off the loan and principal in 6 months or 26 weeks. We use the following formula (similar to mortgage formula):

Weekly payment = Loan * [ r%/52 * (1+r%/52)t]/[(1+r%/52)t - 1]; where r% is the applicable annual rate (16%) and t is the time period (26 weeks). We divide by 52 to convert the rate into weekly rate.

Weekly payment = 2000 * [16%/52 * (1+16%/52)26] / [(1+16%/52)26 - 1] = 80.16. Hence the person will have to pay $80.16 weekly to repay the entire loan at 16% weekly compounded.

(c) The credit card companies usually charge interest on carried forward balances (including interest on interest) in monthly cycles. Since in this case 26 weeks will correspong to a little more than 6 months, the comparison may not be exact , however it will be very close. Moreover the card companies will charge interest till the date of repayment, hence the difference should be miniscule if at all in this case.

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