Compute the specified quantity. Round all answers to the...

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest 0.001\%, as appropriate.
A 5-year bond costs $\$ 1,000$ and will pay a total of $\$ 250$ interest over its lifetime. What is its annual interest rate? [HINT: See Example 3.]

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Key Concepts

Bond Pricing

Bond pricing involves determining the value or cost of a bond at a given point in time, often based on the present value of its expected future cash flows. These cash flows include periodic interest payments and repayment of the face value at maturity, and the price reflects the yield demanded by investors relative to the bond’s risk and market conditions.

Annual Interest Rate

The annual interest rate is a percentage that represents the amount of interest earned or paid in one year relative to the principal amount. For bonds, this rate is often based on the total interest payments received over the life of the bond divided by its purchase price and then adjusted to reflect an annual amount, providing a standardized measure of yield.

Simple Interest Calculation

Simple interest calculation involves computing the interest earned or paid by multiplying the principal amount by an interest rate and the time period over which the interest is applied. In the context of bonds, when the total interest over the life of the bond and the purchase price are known, the simple interest formula can be rearranged to determine the annual interest rate by dividing the total interest by the product of the bond’s price and its duration in years.

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