A bond has a face value of Rs. 200, maturing in 4 years. Coupon rate is 4% p.a. and the bond makes annual coupon payments. If the yield to maturity is 4%, then the present value of the bond is: (use \((1.04)^{-4} = 0.8551\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 200
Let F = 200 be the face value. The annual coupon is C = 4% of 200 = 8, for n = 4 years, at the yield i = 0.04.
The price of a bond is the present value of the coupons (an annuity) plus the present value of the face value:
\( \displaystyle V = C\left[\frac{1-(1+i)^{-n}}{i}\right] + F(1+i)^{-n} \)
\( \displaystyle V = 8\left[\frac{1-0.8551}{0.04}\right] + 200(0.8551) \)
\( V = 8(3.6225) + 171.02 \)
\( V = 28.98 + 171.02 = 200 \)
Shortcut: When the coupon rate equals the yield, the bond is priced at its face value (at par), here Rs. 200.
CBSE Applied Mathematics (Class XII):
Valuation of Bonds
