Final answer:
When interest rates increase, the value of existing bonds with lower rates decreases. Therefore, if interest rates are at 9%, a bond with a 6% coupon rate will sell for less than its face value. The present discounted value determines what an investor should be willing to pay for the bond now.
Step-by-step explanation:
When considering the purchase of a bond one year before its maturity, it is important to understand the effects of interest rate risk. If a $10,000 ten-year bond was originally issued at a 6% interest rate and interest rates have since risen to 9%, the bond price is expected to decrease. The reason is that new investors can find bonds that pay more interest, making the older, lower-yielding bonds less attractive and thus worth less on the market.
To calculate the price you would be willing to pay for the bond (the present discounted value), you need to discount the future bond payments by the current market interest rate. Since the bond has one year left before maturity, you would calculate the present value of one year of interest payments plus the face value of the bond upon maturity. With the higher interest rate of 9%, the discounted price would certainly be less than the face value of $10,000 because the bond's coupon rate is now below the market rate.
This concept emphasizes both the potential loss due to opportunity cost if you had invested in a bond with a lower interest rate before rates rose, and the calculation needed to determine your investment's current value.