Suppose that annual income from a rental property is expected to start at 

​$1 comma 3001,300 

per year and decrease at a uniform amount of 

​$3535 

each year after the first year for the 

1414​-year 

expected life of the property. The investment cost is 

​$7 comma 0007,000​, 

and *i* is 

1010​% 

per year. Is this a good​ investment? Assume that the investment occurs at time zero​ (now) and that the annual income is first received at EOY one.

The present equivalent of the rental income equals

To determine if the rental property is a good investment, we can calculate the Present Equivalent (PE) or the Net Present Value (NPV) of the expected income over the 14-year period and compare it to the initial investment.

### Given:
- Initial annual income $ I_1 = 1300 $ USD
- Annual decrease in income $ d = 35 $ USD
- Expected life of the property $ N = 14 $ years
- Investment cost $ C_0 = 7000 $ USD
- Interest rate $ i = 10\% $ per year

### Approach:

1. **Cash Flow Calculation**:
   The income starts at $ 1300 $ USD for the first year and decreases by $ 35 $ USD each year, forming an arithmetic series. Thus, the income for year $ n $ is:
   \[
   I_n = 1300 - (n - 1) \cdot 35
   \]
   This gives:
   - $ I_1 = 1300 $
   - $ I_2 = 1300 - 35 = 1265 $
   - $ I_3 = 1300 - 2 \cdot 35 = 1230 $
   - ...

2. **Present Value (PV) of Cash Flows**:
   The present value of the income in each year needs to be discounted back to present time using the formula for the present value of a cash flow at year $ n $:
   \[
   PV_n = \frac{I_n}{(1 + i)^n}
   \]
   where $ i = 0.10 $.

3. **Summing the Present Value of All Cash Flows**:
   We calculate the present value for all 14 years, sum them up, and compare it to the initial investment cost.

Let me calculate the present equivalent for you.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you step-by-step to calculate the present value manually or try again later when the tool is available.

Would you like details on how to proceed with manual calculations, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. How is the present value of cash flows calculated in financial analysis?
2. What does a negative NPV indicate about an investment?
3. How does the interest rate impact the present value of future cash flows?
4. What are the advantages of using NPV to evaluate investment decisions?
5. How does a declining income stream affect the overall investment value?

**Tip**: Always compare the NPV of an investment with the initial cost to assess its profitability.

Suppose that annual income from a rental property is expected to start at $1,300 per year and decrease at a uniform amount of $35 each year after the first year for the 14-year expected life of the property. The investment cost is $7,000, and the interest rate is 10% per year. Is this a good investment? Assume that the investment occurs at time zero (now) and that the annual income is first received at EOY one.

Explore how to evaluate the profitability of a rental property investment where annual income starts at $1,300 and decreases by $35 each year over 14 years. Learn how to calculate the present value of future income and determine if the investment is profitable using NPV at a 10% interest rate. Suitable for finance students and professionals.

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