Question

# 5. Imagine that a \$10,000 ten-year bond was issued at an interest rate of 6%. You...

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.

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.

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