Question

In: Finance

Compute the duration of a three-year bond, given an annualcoupon of 7%, and a current...

Compute the duration of a three-year bond, given an annual coupon of 7%, and a current market price of $900. What would be the maturity of a zero-coupon bond with the same duration? (Hint: remember to start with the IRR (YTM) calculation).

Expert Solution

Current Price =900

Coupon 7%

Maturity = 3 years

SInce the Current Price of Bond > Par Value, the TYM will be less than Coupon.

Let's assume the YTM be 11%

Value of Bond =

=

= 902.25

Now,

Let's assume the YTM be 12%

Value of Bond =

=

= 879.91

Using interpolation

YTM =

= 11% + ((902.25 - 900) / (902.25 - 900) + (900 - 879.91)) * (12-11)

= 11% + 10

= 11.10%

Value of ZCB = 1000 / (1+r)^n

r = 0.1110

n = 3

= 1000 / (1+0.1110)^3

=729.22

jeff jeffy answered 2 years ago

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