Question

On October 31, 2011, Simeon Builders borrowed $16 million cash and issued a 7-month, noninterest-bearing note. The loan was made by Star Finance Co. whose stated discount rate is 8%. Sky's effective interest rate on this loan is: (Explain how you got the answer)

a) More than the stated discount rate of 8%
b) Less than the stated discount rate of 8%
c) Equal to the stated discount rate of 8%

Please also explain how you came to your answer

Answer 1

Here the amount of loan is = $ 16,000,000 and the discount rate is given @ 8%. Period is 7 months

Thus the interest component at discount rate For 7 months = Loan amount × rate × period = $ 16,000,000 × 8% × 7/12 = $ 746,667.

Now, the loan was non interest bearing so the amount of $ 16 million will be payable at maturity which means that amount will be inclusive of the notional interest rate of 8% of discount. So to get the actual principal loan without interest we need to exclude the interest amount. I.e Principal = $ 15,253,333( 16,000,000- 746,667)

And for effective interest rate will devide the interest amount as calculated above with the principal loan amount adjusted with the period will give the effective interest rate.

Effective interest rate =( $ 746,667 / 15253333) × 12/7 = $ 8.39 which is higher than the discount rate.

Thus the correct Option is-------------A i.e more than the stated discount rate of 8%