X2 issued callable bonds on january 1, 2015. the bonds pay interest annually on december 31 each year. x2's accountant has projected the following amortization schedule from issuance until maturity:
date cash paid interest
expense decrease in carrying value carrying value
1/12015 $107,167
12/31/2015 $8,755 $8,038 $717 106,450
12/31/2016 8,755 7,984 771 105,678
12/31/2017 8,755 7,926 829 104,849
12/31/2018 8,755 7,864 891 103,958
12/31/2019 8,755 7,797 958 103,000
what is the annual market interest rate on the bonds?

market rate is 7.5%

Explanation:

We will work with the formulas for bonds amortization under effective rate method:

1.-  Face value x rate = cash proceeds

2.- Carring Value x market rate = interest expense

3.- Cash proceds - interest expense = amortization

With the second formula, and the givne value we are able to solve for market rate:

carrying value at 12/31/2015 is used to calcualte the 2016 interest expense:

106,450 x market rate= 7,984

market rate = 7,984/106,450 = 0.07500 = 7.5%

carrying value at 12/31/2016 is used to calcualte the 2017 interest expense:

105,678 x market rate = 7,926 = 0.07500 = 7.5%

So, we can conclude the market rate is 7.5%

the third answer is correct.