Question

Let's denote the price of a non-maturing bond (called a consol) as $P_b$. The equation that indicates this price is $P_b=\frac{I}{r}$, where I is the annual net income the bond generates and r is the nominal market interest rate.

a. Suppose that a bond promises the holder 500$ per year forever. If the nominal market interest rate is 5 per cent, what is the bond's current price?

b. What happens to the bond's price if the market interest rate rises to 10 per cent?

Short answer

a. The bond's current price $\$10000$

b. The bond's price if the market interest rate rises to$10\%$will fall by$\$5000$

Step-by-step solution

introduction

A non-maturing bond or interminability is a non-redeemable bond with no development date. These bonds are treated as value, not obligation and pay a constant flow of interest instalments for eternity.

explanation part (a)

Given,

I =$\$500$

nominal market interest rate r =$5\%$

We know,

role="math" localid="1651664386923" $$\begin{gathered} P_o=\frac{I}{r} \\ \Rightarrow \frac{500}{0.05}=10000 \end{gathered}$$

The bond's current price is$\$10000$

explanation part (b)

if the market interest rate rises to $10$per cent,

$$\begin{gathered} P_0=\frac{l}{r} \\ \Rightarrow \frac{500}{0.10}=5000 \end{gathered}$$

The bond's price if the market interest rate rises to$10\%$ will fall by$\$5000$