Question

Your company has taken out a $100,000 loan over two and a half years with interest initially at 9% per half-year, and payments due at the end of each period. What is the annual interest rate effectively levied on this loan?

A. 16.22%

B. 16.23%

C. 18.56%

D. 18.81%

Answer 1

Answer : (D) 18.81%

Explanation :

Loan taken = $100,000

Interest Rate = 9% per half-year

Calculation of Annual Effective Interest Rate:

r = ( 1 + i / n )ⁿ - 1

Here, r = Annual effective interest rate

i = Annual interest rate ( Annual interest rate = 2 x interest rate for half year)

= (2 x 9) = 18%

n = Number of compounding periods = 2 times in a year

r = ( 1 + 0.18 / 2 )² -1

r = ( 1 + 0.09 )² - 1

r = ( 1.09 )² - 1

r = 1.1881 - 1

r = 0.1881 or say 18.81%

Effective Rate of Interest = 18.81 %