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.**




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:

\[
PV = C \times \left( 1 - \frac{1}{(1 + r)^t} \right) \div r
\]

Where:
- $ PV $ = present value of the annuity
- $ C $ = annual payment ($9,600)
- $ r $ = discount rate (12% or 0.12)
- $ t $ = number of periods (16, 41, 76, or forever)

### 1. Present value for 16 years:
\[
PV_{16} = 9600 \times \left( 1 - \frac{1}{(1 + 0.12)^{16}} \right) \div 0.12
\]

### 2. Present value for 41 years:
\[
PV_{41} = 9600 \times \left( 1 - \frac{1}{(1 + 0.12)^{41}} \right) \div 0.12
\]

### 3. Present value for 76 years:
\[
PV_{76} = 9600 \times \left( 1 - \frac{1}{(1 + 0.12)^{76}} \right) \div 0.12
\]

### 4. Present value if payments occurred forever:
For perpetual payments (a perpetuity), the present value is calculated using the perpetuity formula:

\[
PV_{\infty} = \frac{C}{r} = \frac{9600}{0.12}
\]

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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? What would the value be if the payments occurred for 41 years? What would the value be if the payments occurred for 76 years? What would the value be if the payments occurred forever?

Calculate the present value of an investment offering $9,600 per year for 16, 41, or 76 years, with a required return of 12%. Also, find the present value of perpetual payments. This solution covers the formulas for present value of annuities and perpetuities in finance.

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