Final answer:
The interest on a $10,000, 8%, 1-year note receivable is $800. When interest rates increase, as in the example from 6% to 9%, the price of a bond will decrease to provide the same yield relative to new bonds at higher rates. Consequently, you would pay less than the face value of the bond in a high-interest-rate environment.
Step-by-step explanation:
The interest on a $10,000, 8%, 1-year note receivable is calculated by taking the principle ($10,000) and multiplying it by the interest rate (8%) for the period of time (1 year). Using the formula Interest = Principal × Rate × Time, we get:
Interest = $10,000 × 8% × 1 = $10,000 × 0.08 = $800.
So, the correct answer is b. $800.
Now, if we consider the scenario of changing interest rates and buying a bond, it is crucial to understand that bond prices and market interest rates are inversely related. If you were to buy a bond with fixed interest payments, such as a $10,000 ten-year bond at 6% interest, but the market rates have risen to 9%, the bond's price would decrease since newer issues in the market would offer a higher interest rate. Therefore, buyers would only be willing to purchase the old bond at a discounted price to achieve a yield comparable to the current market rates.
If we use the given information about alternative investments yielding 12%, it is clear that you would not pay the full face value for a bond yielding less than the market interest rate. Instead, you would pay an amount ($964 in this case) that allows the investment to grow to the expected payments ($1,080 from the bond one year from now) when applying the current market interest rate.