Someone has obtained a short-term loan from the Bank. The loan matures in 180 days and is in the amount of $45,000. He hopes to have sufficient backing from other investors by the end of the next 6 months. The Bank offers two financing options for the $45,000 loan: a fixed-rate loan at 2.5% above prime rate or a variable rate loan at 1.5% above prime.
Currently the prime rate of interest is 6.5%, and the consensus forecasts of a group of mortgage economists for changes in the prime rate over the next 180 days are as follows: sixty days from today the prime rate will rise 0.5%; 90 days from today the prime rate will rise another 1%; 180 days from today the prime rate will drop 0.5%.
Using the forecasts prime rate changes: A. Calculate the total interest cost over 180 days for a fixed rate loan B. Calculate the total interest cost over 180 days for a variable rate loan
I was able to calculate (A) correctly:
45000*.09*(180/365)=1,997.26 1997.26/45000=.04438 (1.04438)^(365/180) - 1 = .09205
However, I am having trouble with part (B)
Here's what I've tried:
1st 60 days: .085*(60/365) = .01397
next 30 days: .095*(30/365) = .00781
next 90 days: .09*(90/365)= .02219
(1.04397)^(365/180) - 1 = .09118
However, the correct answer should be .09031
Any help as to where I went wrong would be SO much appreciated. Thanks!!!