A 10-year bond of face value 100 CCU and coupon rate of 8% was issued exactly six years ago. If the yield to maturity today is 7%, what would be the price of the bond today?
To calculate the price of a bond, you need to understand the relationship between bond prices, coupon rates, face values, and yields to maturity. The formula for calculating the price of a bond is as follows:
Bond price = (C × (1 - (1+r)^-n) / r) + (F / (1+r)^n)
Where:
C = Coupon payment
r = Yield to maturity (expressed as a decimal)
n = Number of periods
F = Face value of the bond
In this case, the bond has a face value of 100 CCU and a coupon rate of 8%. The yield to maturity is given as 7%. The bond was issued exactly six years ago, which means it has four years remaining until maturity (10 years - 6 years).
Let's calculate the bond price step by step:
Step 1: Calculate the annual coupon payment
C = Coupon rate × Face value
C = 8% × 100 CCU
C = 8 CCU
Step 2: Calculate the number of periods
n = Number of years remaining until maturity
n = 4
Step 3: Convert the yield to maturity to a decimal
r = Yield to maturity / 100
r = 7% / 100
r = 0.07
Step 4: Plug the values into the bond price formula
Bond price = (C × (1 - (1+r)^-n) / r) + (F / (1+r)^n)
Bond price = (8 × (1 - (1+0.07)^-4) / 0.07) + (100 / (1+0.07)^4)
Now, you can calculate the bond price using a calculator or a spreadsheet.
The current price of the bond would be the sum of the two values calculated using the above formula.