Question

2. Otis “Bad” Blake needs an advance on his next three paychecks, to pay off a $3000 debt he has accumulated from careless spending. Otis is paid every 15 days by the ranch at which he is a cook. Desperate, Otis turns to Guido at Tucumcari Pawn & Paycheck Advance to borrow the $3000. Guido agrees to give Otis the $3000. In return, Otis must provide his Gibson SJ-45 guitar as collateral and also agree to repay Guido $1050 in 15 days, $1050 in 30 days, and $1050 in 45 days, (i.e., on his three paydays). Once Guido receives the final payment, Otis will also be able to retrieve his precious guitar. Otis is thrilled because he thinks that he is only paying 5% interest (3x$50 / $3000) to get out of this bind. Assuming a 360-day year, what is the effective annual rate (EAR) that Guido is actually charging Otis for the paycheck advance?

Answer 1

Answer:

If we assume = Period = 15 days

Equal payment made in each of 3 periods = $1,050

Loan amount = $3,000

We need rate of interest period of 15 days.

Factor of loan amount over equal payment per period for 3 years = $3,000 / $1,050 = 2.8571

If we refer Present Value (PV) Interest Factors for a One-Dollar Annuity for 3 periods ,nearest interest rate for PV factor of 2.8571 , we get is 2.5%

Hence rate of interest charged for 15 days = 2.5%

Effective annual rate = 2.5% * 360/15 = 30%