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 rounded to 2 decimal places.)
  

b. Discounted interest (with no compensating balance). (Input your answer as percent rounded to 2 decimal places.)

c. An installment loan (12 payments). (Input your answer as a percent rounded to 2 decimal places.)

d. Discounted interest with a compensating balance of 4 percent. (Use a 360-day year. Input your answer as a percent rounded to 2 decimal places.)
  
  

Answer 1

Annual Interest rate = 17%

a.

Simple 17 percent interest with a compensating balance of 8 percent.

Effective annual rate = 17% / (1 - 8%)

= 18.48%

Effective annual rate is 18.48%.

b,

Discount interest rate = 17% / (1 - 17%)

= 20.48%

Effective annual rate in case of discount loan is 20.48%.

c.

in installment loan = [(1 + 17% / 12) ^ 12] - 1

= 1.1839 - 1

= 18.39%

Effective rate in case of installment loan is 18.39%.

d.

Discounted interest with a compensating balance of 4 percent

Effective annual rate = 20.48% / (1 - 4%)

= 21.34%

Effective annual rate in case of Discounted interest with a compensating balance of 4 percent is 21.34%.