Question

Your company plans to borrow $13 million for 12 months, and your banker gives you a stated rate of 24 percent interest Calculate the effective rate of interest for the following types of loans a. Simple 24 percent interest with a compensating balance of 10 percent. (Use a 360-day year. Input your answer as a percent rounded to 2 decimal places.) Effective rate of interest b. Discounted interest (with no compensating balance). (Input your answer as a percent rounded to 2 decimal places.) Effective rate of interest c. An installment loan (12 payments). (Input your answer as a percent rounded to 2 decimal places.) Effective rate of interest < Prev 4 of 4EE Next >

Answer 1

a.

Sometimes a bank when offering a loan requires the client to hold a certain amount of money with the bank, this is known as compensating balance. This pushes the effective rate to be higher than the actual interest rate.

Effective rate with compensating balances (c) is = Interest/(1-c)

Interest is 24%, compensating balance is 10%,

=24%/1-0.1

=24/0.9

=26.67%

b.

The effective rate of interest without compensating balance is = Interest /1-interest

=24%/1-0.24

=31.58%

c.

The effective rate on a discounted loan = 2 X Annual # of payments X Interest/(Total no. of payments + 1) X Principal

Interest = 24 % of $13 million =$3,120,000

Effective rate of interest = (3,120,000*2*12)/(13*13,000,000)

=44.31%

d.

Effective Rate of Interest = Interest/(1-compensating balance-interest)

=24% / (1-0.24-0.05)

=33.80%