Questions: If you paid 900 for a 1000 25-year bond that pays a 10% annual interest payment, the bond's yield is 11.1% 5.3% 9% 10%

If you paid 900 for a 1000 25-year bond that pays a 10% annual interest payment, the bond's yield is 11.1% 5.3% 9% 10%
Transcript text: If you paid $\$ 900$ for a $\$ 1000$ 25-year bond that pays a $10 \%$ annual interest payment, the bond's yield is 11.1\% 5.3\% 9\% 10\%
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Solution

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Solution Steps

To find the bond's yield, we need to calculate the yield to maturity (YTM), which is the internal rate of return (IRR) of the bond. The YTM is the interest rate that makes the present value of the bond's future cash flows equal to its current price. The cash flows include the annual interest payments and the face value of the bond at maturity.

To solve this problem, we need to calculate the yield of the bond. The yield of a bond is essentially the return on investment, which can be calculated using the formula for the current yield:

Current Yield=Annual Interest PaymentCurrent Price of the Bond \text{Current Yield} = \frac{\text{Annual Interest Payment}}{\text{Current Price of the Bond}}

Step 1: Calculate the Annual Interest Payment

The bond has a face value of \$1000 and pays a 10% annual interest. Therefore, the annual interest payment is:

Annual Interest Payment=0.10×1000=$100 \text{Annual Interest Payment} = 0.10 \times 1000 = \$100

Step 2: Calculate the Current Yield

The current price of the bond is \$900. Using the formula for current yield:

Current Yield=100900 \text{Current Yield} = \frac{100}{900}

Step 3: Simplify the Current Yield

Simplify the fraction to find the yield as a percentage:

Current Yield=100900=0.1111… \text{Current Yield} = \frac{100}{900} = 0.1111\ldots

Convert this to a percentage:

Current Yield=0.1111×100%=11.11% \text{Current Yield} = 0.1111 \times 100\% = 11.11\%

Final Answer

The bond's yield is approximately 11.1%. Therefore, the correct answer is:

11.1% \boxed{11.1\%}

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