Question

Your local loan shark offers weekly payday loans: You can borrow $1,000 and pay back $1,040 one week later (or lose a finger or two).

1. What is the effective annual rate on the loan? Enter your answer as a decimal and not a percentage.

2. What is the APR on the loan? Enter your answer as a decimal and not a percentage.

Answer 1

Answer 1.

Amount borrowed = $1,000
Amount repaid = $1,040
Period = 1 week

Weekly interest rate = (Amount repaid / Amount borrowed) - 1
Weekly interest rate = ($1,040 / $1,000) - 1
Weekly interest rate = 1.04 - 1
Weekly interest rate = 0.04 or 4.00%

Effective annual rate = (1 + Weekly interest rate)^52 - 1
Effective annual rate = (1 + 0.04)^52 - 1
Effective annual rate = 7.6866 - 1
Effective annual rate = 6.6866

Answer 2.

Annual interest rate = 52 * Weekly interest rate
Annual interest rate = 52 * 0.04
Annual interest rate = 2.08