Question

Payday loans are very short-term loans that charge very high interest rates. You can borrow $400 today and repay $476 in two weeks. What is the compounded annual rate implied by this 19 percent rate charged for only two weeks? (Hint: Compound the 2-week return 26 times for the annual return.) (Do not round intermediate calculations and round your final answer to 2 decimal places.).

Answer 1

Answer:

9109.18%

Explanation:

Data provided in the question:

Interest rate charged for two weeks = 19% = 0.19

Now,

The Annual rate (APR) = ( 1 + i )ⁿ - 1

Here,

r is the interest rate per period = 19%

n = number of periods in a year

In the given question interest is charged every two

also,

there are 52 weeks in a year

Therefore, total number of periods, n = $\frac{52}{2}$ = 26

Therefore,

Annual rate = ( 1+ 0.19 )²⁶ - 1

or

Annual rate = 92.091  - 1 = 91.0918

or

91.0918 × 100 = 9109.18%