A bond has face value of ₹1000 matures in 4 years. Coupon rate 4% per annum. The bond makes annual coupon payments. If the yield to maturity is 4%, then the fair value of bond is :

(Given $(1.04)^{-4}=0.8551$)

₹1000

The correct answer is Option (4) → ₹1000

The fair value of a bond,

$P=∑\frac{C}{(1+r)^t}+\frac{F}{(1+r)^n}$

and,

$PV_{coupons}=C×\left(\frac{1-(1+r)^{-n}}{r}\right)$

$=40×\left(\frac{1-(1.04)^{-4}}{0.04}\right)$

$=40×3.63=142.5$

$PV_{face}=\frac{1000}{(1.04)^{4}}≃854.8$

$P=PV_{coupons}+PV_{face}$

$=145.2+854.8$

$=₹1000$