You borrow $95 today for six and a half weeks. You must repay $100 at loan maturity. What is the effective annual rate on this loan?

Question

Quizplus · Accepted Answer

We can use the formula for effective annual rate:

(1 + EAR) = (1 + periodic rate)^n

Where n is the number of periods in a year. In this case, the loan is for 6.5 weeks, which is approximately 0.125 years (6.5/52). The periodic rate can be found by dividing the total interest paid by the principal borrowed:

$100 - $95 = $5 in interest
$5/$95 = 0.0526

So the periodic rate is approximately 5.26%. Plugging in these values, we get:

(1 + EAR) = (1 + 0.0526)^8
EAR = (1.0526)^8 - 1
EAR = 0.5073 or 50.73%

Therefore, the best choice is A.

You Borrow $95 Today for Six and a Half Weeks