Your cousin is due a tax refund of 400 in six weeks His tax

Your cousin is due a tax refund of $400 in six weeks. His tax preparer has an arrangement with a bank to get him the $400 now. The bank charges an administrative fee of $29 plus interest at 6.5%. What is the actual interest rate for this loan?

Solution

For determining actual interest rate we have to discount 400 @ 6.5% for 42 days(7*6) and deduct $29 fees for actual receipt today.

PV = FV*(1+i)^-n

= 400*(1+6.5%/365)^-42

= 397.0196

Receipt today = 397.0196-29 = 368.0196

So our PV is 368.0196 and FV is 400 , Periods = 42, I = ?

By using same PV formula

368.0196*(1+i)^42 = 400

(1+i)^42 = 400/368.0196 = 1.086899

Taking 42^nd root of both sides

1+i = 1.001986

i = 0.001986 for a day or 72.49% p.a.