What is the duration of a two-year bond that pays an annual coupon of 10.8 percent and has a current yield to maturity of 13.3 percent? Use $1,000 as the face value. (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

The value in the present of a sum of money, in opposition to some future value it will have when it has been invested at compound interest.

Computation of duration:

given,

Annual coupon rate = 10.8%,

Maturity rate = 13.3%, and

Face Value = $1,000.

Cash flow for the 1st year would be:

[tex]\text{Cash Flow} =\text{Face Value}\times\text{Annul Coupun Rate}\\\\\text{Cash Flow} =\$1,000\times\dfrac{10.8}{100}\\\\\text{Cash Flow} =\$108.[/tex]

Then the present value would be:

[tex]\text{Present Value} =\dfrac{ \text{Future Value}}{(1+i)^n}\\\\\\\text{Present Value} =\dfrac{\$108}{(1+13.3\%)}\\\\\\\text{Present Value} = 95.3222.\\[/tex]

For the second year:

[tex]\text{Cash Flow} =\text{Face Value}\times\text{Annul Coupun Rate}\\\\\text{Cash Flow} =(\$1,000+\$108)\times\dfrac{10.8}{100}\\\\\text{Cash Flow} =\$1108.[/tex]

Then the present value at the end of 2 years would be:

[tex]\text{Present Value} =\dfrac{ \text{Future Value}}{(1+i)^n}\\\\\\\text{Present Value} =\dfrac{\$1,108}{(1+13.3\%)}\\\\\\\text{Present Value} = 863.1674.[/tex]

Then the duration of the bond would be:

[tex]\text{Duration Of Bound}= \dfrac{(95.3222\times1)+(863.1374\times2)}{(95.3222+863.1374)}\\\\\text{Duration Of Bound}=1.9 \text{Years}.\\[/tex]

Therefore, the duration of the bound would be 1.9 years.

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