Question

A zero-coupon bond with a 2-year maturity and face value of $1,000 is trading at $975. What is this bond's yield to maturity? Round to the nearest tenth of a percent (e.g. 4.32% = 4.3). Numeric Answer:

Answer 1

Solution:

The Yield to Maturity of a zero coupon bond can be calculated using the following formula

YTM = r = (Face value / Current Price)^{(1/ Years to maturity )} - 1

As per the Information given in the question we have

Face value of the bond = $ 1000

Current price of the bond = $ 975

Years to maturity = 2 years

Applying the above values in the formula we have

= ( 1000 / 975 ) ^{( 1/ 2 )} – 1

= ( 1.025641 ) ^{( 0.5 )} – 1

= 1.012739 – 1

= 0.012739

= 1.2739 %

= 1.3 % ( when rounded off to the nearest tenth of a percent )

Thus the Yield to maturity of the zero coupon bond = 1.3 %

Note : ( 1.025641 ) ^{( 0.5 )} = 1.012739 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.025641,0.5)