-1

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!!!

0

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.