Question

an investment offers $6,000 per year, with the first payment occurring one year from now. the required return is 5 percent. a. what would the value be today if the payments occurred for 10 years? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. what would the value be today if the payments occurred for 35 years? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. what would the value be today if the payments occurred for 65 years? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. what would the value be today if the payments occurred forever? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Step-by-step explanation:

The formula for the present value of annuity can be represented as:

PV=Payment×1−(1+r)−^n/r

Here:

Present value (PV) has to be calculated.

Payment = $6,000

r (rate) = 5% or 0.05

n = 10

Substituting the values we have:

PV=$6,000×1−(1+0.05)−10/0.05

Present Value = $46,330.41.

For 35 years:

PV=$6,000×1−(1+0.05)−35/0.05

Present Value = $98,245.17

For 65 years:

PV=$6,000×1−(1+0.05)−65/0.05

Present Value = $114,966.42

For perpetuity:

Value of perpetuity = Cash flow / Rate

= $6,000 / 0.05 = $120,000