Math Problem Statement
An investment offers $9,600 per year for 16 years, with the first payment occurring one year from now. Assume the required return is 12 percent.
What is the value of the investment today?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
What would the value be if the payments occurred for 41 years?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
What would the value be if the payments occurred for 76 years?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
What would the value be if the payments occurred forever?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
Solution
To calculate the present value of the investment, we are dealing with an annuity. Since the payments occur annually and the first payment is one year from now, we will use the formula for the present value of an ordinary annuity:
Where:
- = present value of the annuity
- = annual payment ($9,600)
- = discount rate (12% or 0.12)
- = number of periods (16, 41, 76, or forever)
1. Present value for 16 years:
2. Present value for 41 years:
3. Present value for 76 years:
4. Present value if payments occurred forever:
For perpetual payments (a perpetuity), the present value is calculated using the perpetuity formula:
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Math Problem Analysis
Mathematical Concepts
Finance
Present Value
Annuities
Perpetuities
Formulas
PV = C × [(1 - 1 / (1 + r)^t) / r]
PV_perpetuity = C / r
Theorems
Present Value of an Ordinary Annuity
Present Value of a Perpetuity
Suitable Grade Level
College-Level Finance
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