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?

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Respuesta :

TomShelby TomShelby · Answer 1 · 2019-09-15T18:53:17+02:00

Answer:

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%