Question

Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000. Use semi-annual periods. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Solve for the fill in the blanks.

	Price Maturity (years) Yield to Maturity $440 20 % $540 20 % $540 10 % 10 10.40 % 10 7.60 % $440 8.40 %

Answer 1

We will solve first 3 blank spaces in Yield to Maturity column

Since these are Zero-coupon bonds at a par value of 1000, we will use below formula in all the calculations

P₀ = Par Value / (1 + YTM)^T

First Blank in YTM: Price = 440 and Time = 20

Using the formula, 440 = 1000 / (1+YTM)²⁰

=> (1+YTM)²⁰ = 1000 / 440

=> YTM = (1000 / 440)^1/20 - 1

=> YTM = 4.19%

Second Blank in YTM: Price = 540 and Time = 20

Using the formula, 540= 1000 / (1+YTM)²⁰

=> YTM = (1000 / 540)^1/20 - 1

=> YTM = 3.13%

Third Blank in YTM: Price = 540 and Time = 10

Using the formula, 540= 1000 / (1+YTM)¹⁰

=> YTM = (1000 / 540)^1/10 - 1

=> YTM = 6.36%

Now we will work blanks in Price column

First Blank in Price: Time = 10 and YTM = 10.4%

Since Par value = 1000

Price = 1000 / (1+10.4%)¹⁰ = 371.80

Second Blank in Price: Time = 10 and YTM = 7.60%

Price = 1000 / (1+7.60%)¹⁰ = 480.70

Moving to last blank which is in Time column: Price = 440 and YTM = 8.40%

Using the formula: => 440 = 1000 / (1+8.40%)^T

=> (1.0840)^T = 1000 / 440

Putting Log₁₀ on both sides of the equation

=> T * Log10 (1.0840) = Log10 (1000/440)

=> T = Log10 (1000/440) / Log10 (1.0840) = 0.35655 / 0.035029 = 10.18 (round 10)