Question

5. Imagine that a $10,000 ten-year bond was issued at an interest rate of 6%. You are thinking about buying this bond one year before the end of the ten years, but interest rates are now 9%.

a. Given the change in interest rates, would you expect to pay more or less than $10,000 for the bond?

b. Calculate what you would actually be willing to pay for this bond.

Answer 1

ans...

(a)

There exists an inverse relationship between bond prices and interest rates.

An increase in interest rates results in a fall in bond prices while a decrease in interest rates results in a rise in bond prices.

In given case, interest rate has increased from 6% to 9%.

Since, interest rate has increased, bond prices will fall.

Thus, given the change (increase) in interest rate, we would be expected to pay less than $10,000 for the bond.

(b)

Face value of ten-year bond (FV) = $10,000

Coupon interest rate (r) = 6% or 0.06

Annual interest = FV * r = $10,000 * 0.06 = $600

New interest rate = 9% or 0.09

Calculate new price of bond -

New price of bond = Annual interest/New interest rate = $600/0.09 = $6,666.67

We would be willing to pay $6,666.67 for this bond.