Math Problem Statement

A bond had a price of $1,946.05 at the beginning of the year and a price of $1,979.47 at the end of the year. The bond's par value is $2,000 and its coupon rate is 5.2 percent. What was the percentage return on the bond for the year?

Multiple Choice

5.25%

7.06%

7.53%

6.18%

1.69%

Solution

To calculate the bond’s percentage return for the year, we need to determine both the capital gain and the income from the bond. Here’s the step-by-step solution:

  1. Capital Gain: The capital gain is the difference between the ending and beginning prices. Capital Gain=1,979.471,946.05=33.42\text{Capital Gain} = 1,979.47 - 1,946.05 = 33.42

  2. Coupon Payment: The bond’s coupon rate is 5.2%, so the annual coupon payment is calculated as follows: Coupon Payment=2,000×0.052=104\text{Coupon Payment} = 2,000 \times 0.052 = 104

  3. Total Dollar Return: This is the sum of the capital gain and the coupon payment. Total Dollar Return=33.42+104=137.42\text{Total Dollar Return} = 33.42 + 104 = 137.42

  4. Percentage Return: To find the percentage return, divide the total dollar return by the beginning price and multiply by 100. Percentage Return=(137.421,946.05)×1007.06%\text{Percentage Return} = \left(\frac{137.42}{1,946.05}\right) \times 100 \approx 7.06\%

Answer:

The percentage return on the bond for the year is 7.06%.

Would you like further details on any step?

Here are some related questions:

  1. How does the coupon rate affect the bond’s yield?
  2. What is the difference between capital gain and coupon payment in bond returns?
  3. How would a change in the bond’s price impact the percentage return?
  4. What role does the par value play in determining the coupon payment?
  5. Why is the beginning price used as the base for calculating percentage return?

Tip: When evaluating bond returns, always consider both price appreciation (or depreciation) and coupon payments for an accurate yield.

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Math Problem Analysis

Mathematical Concepts

Finance
Percentage Return
Bond Yield

Formulas

Capital Gain = Ending Price - Beginning Price
Coupon Payment = Par Value × Coupon Rate
Total Dollar Return = Capital Gain + Coupon Payment
Percentage Return = (Total Dollar Return / Beginning Price) × 100

Theorems

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Suitable Grade Level

College-Level Finance or Advanced High School