Final answer:
The price of a bond when its interest rate is less than the market interest rate is based on the present value of its future payments. In the example given, the bond price would not exceed $964 if the market interest rate is 12%. Additionally, the impact of compound interest over time can significantly increase the amount of money accrued compared to simple interest.
Step-by-step explanation:
Understanding Bond Pricing and Interest Rates
When calculating the price of a bond when its interest rate is less than the market interest rate, we must consider how much the expected future payments are worth in today's terms. If you are expected to receive $1,080 from the bond in one year and the market interest rate is 12%, you would need to invest $964 today to get that amount in a year. The calculation is $964(1 + 0.12) = $1080. Therefore, you will not pay more than $964 for the bond originally worth $1,000. This reflects the concept that the present value of money is less when the market interest rates are high.
Similarly, when considering the future payments from a firm, the present value formula can be applied. If a firm promises to pay $15 million now, $20 million in one year, and $25 million in two years, the present value of these payments will be different based on the interest rate applied. A higher interest rate would decrease the present value of these future payments.
When comparing simple interest and compound interest, the key difference is that compound interest includes interest on the accumulated interest of the principal, while simple interest does not. Over time, particularly for large sums, compound interest will accrue significantly more than simple interest.