# Unsecured sources of short term loans (variable and fixed rates)

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

.01397+.00781+.02219=.04397

(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!!!

## 1 Answer

For part B, your first 60 days should be using the prime interest rate 6.5% + 1.5%

Then the rate will rise 0.5% for days 60-90: 7.0% + 1.5%

Then the rate will rise another 1% for days 90-180: 8.0% + 1.5%

The loan matures at 180 days, so the rate change does not matter past day 180.

• To clarify where you went wrong, you had the rate change occur from day 0-60, but the text states that "the rate changed 60 days from today" which would mean from day 60 until the next rate change occurs ( at 90). – Shorlan Apr 25 at 23:59