Question

Jan buys a​ $1,100, 3%​ semi-annual coupon bond for a price of​ $1,000 and holds it to maturity in six years. What was the​ bond's yield to maturity if rates are compounded​ semi-annually?

Answer 1

Face Value = 1100

Semi -annual Coupon Amount = 3% * 1100 = 33

Number of payments = 6*2 = 12

Current Price = 1000

We know that,

Price of the bond = Present value of all semi-annual coupon and face value discounted at semi-annual ytm.

1000 = 33/(1+ytm/2)^1 + 33/(1+ytm/2)^2 + 33/(1+ytm/2)^3 + 33/(1+ytm/2)^4 + 33/(1+ytm/2)^5 + 33/(1+ytm/2)^6 + 33/(1+ytm/2)^7 + 33/(1+ytm/2)^8 + 33/(1+ytm/2)^9 + 33/(1+ytm/2)^10 + 33/(1+ytm/2)^11 + 33/(1+ytm/2)^12 + 1100/(1+ytm/2)^12

We will use heat and trial method to get that value for which above equation satisfy.

ytm / 2 = 3.965

ytm = 7.93% Answer

Or using financial calculator:

N= 12

FV = 1100

PV = -1000

PMT = 33

CPT I/Y

YTM/2 = 3.965

ytm = 7.93% Answer

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