Final answer:
If interest rates increase, you would pay less than the bond's face value; the exact amount depends on a present value calculation at the new interest rate. For a $10,000 return in ten years at a 10% annual compound rate, present value calculation is also needed to find the initial investment amount.
Step-by-step explanation:
When it comes to bond investments, market interest rates play a pivotal role in dictating bond prices. In the scenario you provided, a local water company issued a $10,000 ten-year bond with an interest rate of 6%. If you're considering buying this bond one year before its maturity, and currently, interest rates have risen to 9%, you would expect to pay less than $10,000 for the bond.
This is because the bond's fixed interest payments are less attractive when new bonds are offering higher interest rates; hence, its price decreases to make it a more competitive investment.
To calculate the price you'd be willing to pay for the bond, consider the single coupon payment you will receive in a year and the principal amount you will get at maturity. The present value of these future cash flows should be discounted at the new market interest rate of 9%.
However, without the formula or a financial calculator, we cannot provide the exact amount. Typically, a financial calculator or spreadsheet software would simplify this process.
Switching focus to savings and interest, if you desire $10,000 in ten years from a bank account with an interest rate of 10% compounded annually, you need to find the present value of $10,000 discounted back ten years at 10%. This calculation is also made easy with financial calculators or software.