A man buys a corporate bond from a bond brokerage house for $925. The bond has a face value of $1000 and a 4% coupon rate paid semiannually. if the bond will be paid off at the end of ten years, what rate of return will the man receive?
To calculate the rate of return on a corporate bond investment, we need to consider both the bond price and the coupon payments received.
First, let's calculate the total coupon payments received over the ten-year period.
The bond has a face value of $1000 and a coupon rate of 4%. Since the coupon payments are paid semiannually, we will receive two coupon payments per year for a total of 20 payments over ten years.
Each coupon payment can be calculated as follows:
Coupon Payment = Face Value * Coupon Rate / 2
= $1000 * 0.04 / 2
= $20
Therefore, the total coupon payments received will be:
Total Coupon Payments = Coupon Payment * Number of Payments
= $20 * 20
= $400
Now, let's calculate the total return on the bond by summing up the coupon payments and the face value at the end of ten years.
Total Return = Total Coupon Payments + Face Value - Bond Purchase Price
= $400 + $1000 - $925
= $475
Finally, to determine the rate of return, we need to calculate the annualized rate of return. Since the investment was held for ten years, we can use the compound interest formula:
Rate of Return = [(Total Return / Bond Purchase Price) ^ (1 / Number of Years)] - 1
= [(475 / 925) ^ (1 / 10)] - 1
Using a calculator or spreadsheet, we can find that:
Rate of Return ≈ 0.0239 or 2.39%
Therefore, the man will receive a rate of return of approximately 2.39% on his corporate bond investment.