Question

12. Assume that an investor wishes to purchase a 20-year bond with a maturity value of $1,000 and the coupon payments is 7% of maturity value. The interest is paid semiannually. If the investor requires a 10 percent simple yield to maturity on this investment, what is the maximum price she should be willing to pay for the bond? (Round the answer to the nearest whole number.)​

Group of answer choices

$619

$674

$743

$828

$902

Answer 1

The maximum price is computed as shown below:

= Coupon payment x [ [ 1 - (1 / (1 + r)ⁿ ] / r ] + $ 1,000 / (1 + r)ⁿ

The coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (Since the payment is semi annual, hence divided by 2)

= $ 35

The r is computed as follows:

= 10% / 2 (Since the payment is semi annual, hence divided by 2)

= 5% or 0.05

The n is computed as follows:

= 20 x 2 (Since the payment is semi annual, hence multiplied by 2)

= 40

So, the price of the bond will be:

= Coupon payment x [ [ 1 - (1 / (1 + r)ⁿ ] / r ] + $ 1,000 / (1 + r)ⁿ

= $ 35 x [ [ 1 - (1 / (1 + 0.05)⁴⁰ ] / 0.05 ] + $ 1,000 / 1.05⁴⁰

= $ 35 x 17.15908635 + $ 142.0456823

= $ 743 Approximately

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