Question

A bond has a $1,000 par value, 15 years to maturity, and a 8% annual coupon and sells for $1,080. What is its yield to maturity (YTM)? Round your answer to two decimal places.

Answer 1

YTM = 7.27%

Step-by-step explanation:

We know,

Yield to Maturity (YTM) =
`(I + (M - V_(0) )/(n) )/((2M + V_(0))/(3))`

Here,

I = Coupon Payment = Coupon Rate × Par Value

M = Par Value

`V_(0)` = Market value/Current value

n = Number of years/periods.

Given,

M = $1,000

`V_(0)` = $1,080

I = $1,000 × 8% = $80

n = 15 years

Putting the values into the formula, we can get...

Yield to Maturity (YTM) =
`(I + (M - V_(0) )/(n) )/((2M + V_(0))/(3))`

or, YTM =
`(80 + (1,000 - 1,080)/(15) )/((2*1,000 + 1,080)/(3))`

or, YTM =
`(80 - 5.33)/(1,026.67)`

or, YTM = 0.072730

Therefore, YTM = 7.27%