Question

You bought a 3-year coupon bond for 11,000 today. It has a coupon rate of 10% and a Face Value of 10,000. (assume annual payments end of the year) a. Write out the formula you would use to determine the Yield to Maturity on this bond.

Answer 1

Given for the bond,

Price = $11000

Face value = $10000

Coupon = 10% of 10000 = $1000

time to maturity = 3 year

Let YTM be r for the bond. So, price of the bond today is sum of PV of all future cash flows.

So, Pv = C/(1+YTM) + C/(1+YTM)^2 + C/(1+YTM)^3 + FV/(1+YTM)^3

So, 11000 = 1000/(1+r) + 1000/(1+r)^2 + 11000/(1+r)^3

formula used to determine the Yield to Maturity on this bond is

11 = 1/(1+r) + 1/(1+r)^2 + 11/(1+r)^3