Final answer:
If interest rates rise, the price of pre-existing bonds falls. Therefore, if the interest rates rise to 9% from 6%, the bond will be worth less than its face value of $10,000. By calculating the present value of the bond's cash flows, we find out that you should be willing to pay approximately $9,724.77 for the bond.
Step-by-step explanation:
The question posed relates to the expected price you would pay for a $10,000 ten-year bond issued at a 6% interest rate, considering you want to buy it a year before maturity when the market interest rates are at 9%. The price of a bond inversely relates to the interest rates: when interest rates go up, the price of bonds go down because new bonds are issued at this higher rate, making them more attractive than old ones with lower rates. Therefore, you would expect to pay less than the face value of $10,000 for the bond because it yields lower interest than the prevailing market rate.
To calculate the price you should be willing to pay for the bond, you need to find the present value of the bond's cash flows, which include the final year's interest payment of $600 (6% of $10,000) and the principal amount of $10,000 that you will get back at maturity.
Using the formula for present value, where PV = C / (1+r)^n, C is the cash flow, r is the interest rate (9% or 0.09 in this case), and n is the number of periods (1 year until maturity), the calculations would be as follows:
- Present Value of interest payment: PV = $600 / (1+0.09)^1 = $550.46
- Present Value of principal amount: PV = $10,000 / (1+0.09)^1 = $9174.31
Adding these two amounts gives you the value you should be willing to pay for the bond today:
$550.46 (interest) + $9,174.31 (principal) = $9,724.77
Therefore, the amount you should be willing to pay for the bond is approximately $9,724.77.