Question

Assume the​ zero-coupon yields on​ default-free securities are as summarized in the following​ table: Maturity 1 year 2 years 3 years 4 years 5 years ​Zero-Coupon Yields 4.104.10​% 4.604.60​% 4.904.90​% 5.305.30​% 5.505.50​% What is the price of a​ three-year, default-free security with a face value of $ 1 comma 000$1,000 and an annual coupon rate of 5 %5%​? What is the yield to maturity for this​ bond? What is the price of a​ three-year, default-free security with a face value of $ 1 comma 000$1,000 and an annual coupon rate of 5 %5%​?

Answer 1

Face value or future value of the securities =$1000

Coupon payment = 5% of $1000 or $50

Price of the bond can be calculated as:

Bond price = $50/(1+0.0410) + $50/(1+0,0461)^2 + $1050/(1+0.04904)^3

= $1003.356

Yield to maturity can be calculated as

$1003.356 = $50/(1+y) + $50/(1+y)^2 + $1050(1+y)^3

where, y = yield to maturity

It can be calculated using excel or financial calculator and the value will yield to maturity will be = 4.88%.