Final answer:
The price of a bond will typically decrease if market interest rates rise above the bond's fixed rate. In the example, with interest rates increasing from 6% to 9%, a bond originally worth $10,000 would now be valued at $9,633.03 a year before its maturity, as it is discounted at the higher current interest rate.
Step-by-step explanation:
Understanding Bond Valuation in Relation to Interest Rate Changes
When considering the purchase of a bond close to its maturity date, it is essential to understand how changes in the market interest rate can affect the price of the bond. If interest rates increase, the price of a bond with a fixed interest rate typically decreases. This is because investors can receive a higher interest rate in the new market environment, making the lower fixed interest rate of the existing bond less attractive, and therefore, its price drops to compensate for the lower rate.
Let's apply this concept to a specific example:
A local water company issued a $10,000 ten-year bond at a 6% interest rate.
You are considering purchasing this bond one year before its maturity, but the current market interest rate has risen to 9%.
Given the risen interest rate:
You would expect to pay less than $10,000 for the bond due to the higher current interest rates compared to the bond's fixed rate.
To calculate what you should actually be willing to pay, you would discount the bond's remaining cash flows, which include the final interest payment and the principal repayment at maturity, at the current market rate of 9%.
The calculation is:
Present Value (PV) = Future Value (FV) / (1 + r)n
Where FV is the sum of the final interest payment ($600) plus the bond's face value ($10,000), r is the current market interest rate (9% or 0.09), and n is the number of periods until maturity (1 year).
The PV then becomes:
PV = ($600 + $10,000) / (1 + 0.09)1 = $9,633.03
So, you would be willing to pay $9,633.03 for the bond.