As an investor, you are considering buying a bond that pays 7% semiannual coupon. this bond has a $10,000 face value and will mature in 25 years. if your required rate of return is 5.8% for bonds in this risk class, what is the highest price you would be willing to pay?

The highest price you would be willing to pay is $11,573.53

Explanation:

                                                                            Annual          Semiannual

Face value                                                       10000              10000

Yield to Maturity or required rate of return        5.800%         2.90%

Maturity Period                                                   25                    50

Coupon Rate                                                          7.00%          3.50%

Coupon paid                                                         $700.00        $350.00

PV of coupon payments = $9,178.94

PV of Maturity Value = $2,394.59

Price of Bond= $11,573.53

Therefore, The highest price you would be willing to pay is $11,573.53

The highest price to pay is $9,145.87

Explanation:

P = ∑ C/(1 + Y )∧t. + F/ ( 1 + Y)∧T

Where C = The periodic coupon payment

Y = The yield to maturity

F = The bond par or face value

t = Time

T = The number of periods until the bond's maturity date

Since the bond pays 7% semi- annually, we will divide 7%/2 = 3.5%, and multiply 25 years by 2 = 50 years

Therefore C = 3.5 × 10,000 = 35,000, T = 50, Y = 5.8/100 = 0.058

P = ∑ 35,000/ ( 1 + 0.058)∧25 + 10,000/( 1 + 0.058)∧50

P = ∑ 35,000 / ( 1.058)∧25 + 10,000/ ( 1.058)∧50

P = ∑ 35,000/( 4.0939420648) + 10,000/ ( 16.7603616303)

P = ∑ 8, 549.22 + 596.65

= 9,145.87

The highest price the investor will be willing to pay $ 9,145.87

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