P1510 similar to Question Help Unsecured sources of shortter

P15-10 (similar to)

Question Help

Unsecured sources of short-term loansPersonal Finance ProblemJohn Savage has obtained a short-term loan from First Carolina Bank. The loan matures in

180days and is in the amount of$45,000.

John needs the money to cover start-up costs in a new business. He hopes to have sufficient backing from other investors by the end of the next

6 mnths. First Carolina Bank offers John two financing options for the$ 45000 loan: a fixed-rate loan at 2.7%above the prime rate, or a variable-rate loan at 1.6%.

above prime.Currently, the prime rate of interest is 6.4 %, and the consensus interest rate forecast of a group of economists is as follows: 60 days from today the prime rate will rise by 0.5%; 90 dys from today the prime rate will rise another 1.4%; 180 days from today the prime rate will drop by 0.2%.

Using the forecast prime rate changes, answer the following questions. Assume a 365-day year.

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.

c.Which is the lower-interest-cost loan for the next 180 days?

Solution

a. Calculation of total interest cost over 180 days for a fixed-rate loan:-

Loan Amount = $ 45000

Fixed Rate of Interest = Prime Rate + 2.7% =6.4% + 2.7%= 9.1% p. a.

Total Interest cost for 180 days = $ 45000 * 9.1% * 180/365 =$ 2019.45

b. Calculation of total interest cost over 180 days for a variable-rate loan:-

Variable rate of interest = Prime rate + 1.6%

Current Prime rate = 6.4%

so, Current Variable rate = 6.4% + 1.6% = 8% p.a. applicable for 60 days

Interest for first 60 days = $ 45000 * 8% * 60/365 = $ 591.78

Variable Rate for next 30 days =( 6.4% + 0.5%) + 1.6% = 8.5 % p. a.

Interest for next 30 days =$ 45000 * 8.5% * 30/365 =$ 314.38

Variable Rate for next 90 days =( 6.4% + 0.5% +1.4%) + 1.6% = 9.9% p. a.

Interest for next 90 days =$ 45000 * 9.9% * 90/365=$ 1098.49

Total Interest Cost for 180 days under variable rate loan = 591.78 + 314.38 + 1098.49 = $ 2004.65

c. Fixed Interest Rate for next 180 days = Prime rate + 2.7 % = (6.4% - 0.2%)+ 2.7% = 8.9% p. a.

Variable Rate for next 180 days = (6.4% - 0.2%) + 1.6% = 7.8% p. a.

So, Variable Rate loan is the lower interest cost loan for next 180 days.