Question

Your company plans to borrow $5 million for 12 months, and your banker gives you a stated rate of 17 percent interest Calculate the effective rate of interest for the following types of loans. a. Simple 17 percent interest with a compensating balance of 8 percent (Use a 360-day year. Input your answer as a percent rounde Effective rate of interest 18.48% b. Discounted interest (with no compensating balance). (Input your answer as 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 18.39%

Answer 1

a)

With a compensating balance of 8%, the net loan amount = gross loan amount - compensating balance.

Net loan amount = $5 million - ($5 million * 8%) = $4,600,000.

Interest expense = gross loan amount * interest rate

Interest expense = $5 million * 17% = $850,000.

Effective interest rate = interest expense / net loan amount.

Effective interest rate = $850,000 / $4,600,000

Effective interest rate = 18.48%.

b)

With discounted interest, interest is deducted from the amount the borrower receives at the beginning of the loan.

Amount received by borrower = $5,000,000 - ($5,000,000 * 17%) = $4,150,000.

Effective interest rate = (gross loan amount / amount received by borrower) - 1

Effective interest rate = ($5,000,000 / $4,150,000) - 1

Effective interest rate = 20.48%.

c)

Effective rate = (1 + (interest rate / 12))¹² - 1 (since there are 12 payments, the monthly interest rate = annual interest rate / 12).

Effective rate = (1 + (17% / 12))¹² - 1

Effective rate = 18.39%