Question

The Price Perpetual Bank has purchased a bond that has a coupon rate of 5.5% and a face value of $1000. It has 11 years to maturity and is selling in the market for $887.52. The bond makes annual coupon payments. What is the yield to maturity on this bond?

Answer 1

Answer:

Explanation:

What is given:

FV=1000

PV=887.52

n=11

PMT(coupon) = 0.055*1000 = 55 or C in the formula

Need to find YTM?

Formula to be used is YTM = [C+ (F-P) / n] / [(F+P) / 2]

YTM = [55 + (1000-887.52)/11]/[(1000+887.52)/2)] = [55+10.225]/[943.76]=0.069=6.9%

Answer 2

Answer: 1.09% per annual

Explanation: firstly we are given the face vale of the bond which is $1000

thereafter we are also given the number of years it takes for this bond to mature which is 11 years that is our n in the formula. we are also given the current price of the bond which is $887.52 which these values we can use to calculate the yield to maturity which is a percentage it can take to mature.

we then use the formula for the yield to maturity that comes from the formula: $Face Value=Current Price(1+YTM)^n$

so we rearrange it so that the YTM( yield to maturity) can be the subject of the equation as its the unknown value we are looking for:

$YTM= n\sqrt[n]{Face value/ current price} -1$

YTM = $\sqrt[11]{ 1000/ 887.52} -1$

Yield to maturity is 0.01090670576 which is rounded off to 1.09% per annum.