Question

Consider a zero-coupon bond with 20 years to maturity. The amount that the price of the bond will change if its yield to maturity decreases from 7% to 5% is closest to:

	a.	$53
	b.	$673.
	c.	$118.
	d.	-$53
	e.	$111.

Answer 1

Pricing of a Zero Coupon Bond:

From the information given in the question above, we have:

Time to maturity(n) = 20 years

YTM(r) = 7% to 5%

Face value = $1000(suppose)

Formula: Price of Zero-Coupon Bond = Face value / ( 1 + r)^n

where, r = rate of interest (YTM)

n = time to maturity

(i). When YTM was 7%:

Price of Bond = $1000 / (1 + 0.07)^20

Price = $1000 / (1.07)^20

or, = $1000 / 3.8696

Price = $258.42

(ii). When YTM was 5%:

Price of Bond = $1000 / (1 + 0.05)^20

Price = $1000 / (1.05)^20

or, = $1000 / 2.6533

Price = $376.90

The change in the price of the bond after the decrease in the YTM from 7% to 5% = ($376.90 - $258.42) = $118.48

Therefore bond price will increase $118.48.

Hence, Option(c) is closest to the price that we have calculated in this case.