What would you pay for a $50,000 debenture bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a yield of: (Round computations to 2 decimal places and use the rounded amounts to calculate the final answer. Round the final answer to 2 decimal places.

(a) 8%?

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To calculate the price you would pay for the debenture bond, you need to determine the present value of the future cash flows it will generate.

In this case, the bond pays $5,000 a year in interest for the next 15 years, plus the $50,000 face value at maturity.

To calculate the price at an 8% yield, you would discount each cash flow at a rate of 8%. Here's how you can calculate it step by step:

Step 1: Calculate the present value of the annual interest payments. Since the bond pays $5,000 per year for 15 years, you can use a present value of an ordinary annuity formula to calculate its value.

PV = PMT × [1 - (1 + r)^(-n)] / r

PMT = $5,000 (annual interest payment)
r = 8% (yield expressed as a decimal)
n = 15 (number of years)

PV = $5,000 × [1 - (1 + 0.08)^(-15)] / 0.08
PV ≈ $46,729.43

Step 2: Calculate the present value of the face value at maturity. The face value is $50,000, but since it will be received in 15 years, it needs to be discounted to its present value.

PV = FV / (1 + r)^n

FV = $50,000 (face value)
r = 8% (yield expressed as a decimal)
n = 15 (number of years)

PV = $50,000 / (1 + 0.08)^15
PV ≈ $14,090.58

Step 3: Calculate the total price you would pay for the bond by summing up the present values of the interest payments and the face value.

Total Price = PV of interest payments + PV of face value
Total Price = $46,729.43 + $14,090.58
Total Price ≈ $60,820.01

So, if you wanted to earn an 8% yield, you would need to pay approximately $60,820.01 for the $50,000 debenture bond.