Josh needs $320 to pay off his cell phone. He can use his credit card, but...

Josh needs $320 to pay off his cell phone. He can use his credit card, but the $320 payment will put him at his card limit. His other option is to take out a payday loan. His credit card has an annual rate of 16.8% compounded daily. The payday loan charges a daily rate of 0.75%. Calculate the cost of both options if he will pay both off when he receives his next pay cheque in 3 weeks.

Solutions

Expert Solution

Payment = $320

a. Credit card annual rate compounded daily = 16.8%

Thus, effective annual rate = ((1+16.8%/365)^365)-1 = 18.29% per annum or 0.0501% per day (18.29%/365)

Interest cost if credit card is used = Total Payment including Interest for 3 weeks - $320

Total Payment including Interest for 3 weeks = $320*(1+0.0501%)^21 (3 weeks equals 21 days (3*7 days a week)

= ($320*1.010574) = $323.3837

Interest cost if credit card is used = $323.3837 - $320 = $3.3837 or $3.38

b. Payday loan interest = 0.75% daily

Total interest cost for 3 weeks or 21 days = $320*0.75%*21 = $50.4

Josh should avoid taking payday loan and instead use his credit card as the payday loan cost ($50.4) is significantly higher than the interest on credit card which is only $3.38.

Payday loans are short term unsecured loans which are provided at very high interest rates to meet short term financial obligations. In the given question, the interest rate of pay-day loan is 0.75% daily which is substantially higher than the 0.0501% interest charged on credit card and this leads to the higher cost for pay-day loans.

jeff jeffy answered 1 year ago

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