A bond promises to pay Rs 110 at the end of one year and nothing else. The market rate of interest falls from 10 per cent to 5 per cent. What happens to the price of the bond and to its holder?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The price rises from Rs 100 to about Rs 104.76, and the holder makes a capital gain.
In equilibrium the price of a bond equals its present value. Present value is the sum which, kept at the market rate of interest, grows to what the bond pays.
The price at each rate is its present value:
\( \displaystyle \text{At 10\%: } \frac{110}{1.10} = 100 \)
\( \displaystyle \text{At 5\%: } \frac{110}{1.05} \approx 104.76 \)
The value of her bond rises by about Rs 4.76. A rise in the value of wealth due to a higher bond price is a capital gain.
A fall in the rate of interest raises bond prices, since the two are inversely related.
NCERT (2026-27): “The Speculative Motive … This amount, Rs X, is called the present value of Rs 10 discounted at the market rate of interest. … It is clear that under competitive assets market condition the price of a bond must always be equal to its present value in equilibrium. Now consider an increase in the market rate of interest from 5 per cent to 6 per cent. The present value, and hence the price of the same bond, will become … It follows that the price of a bond is inversely related to the market rate of interest.” Glossary: “Capital gain/loss – Increase or decrease in the value of wealth of a bondholder due to an appreciation or reduction in the price of her bonds in the bond market.” |