Suppose that annual income from a rental property is expected to start at ​$1,100 per year and decrease at a uniform amount of ​$45 each year after the first year for the 15​-year expected life of the property. The investment cost is ​$7,000​, and i is 9​% 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.

It is not a good investment because  

∑ yearly incomes < Final cost of investment

i.e.  $11775  <  $16450

Explanation:

Cost of investment ( principal ) = $7000

Interest rate ( r ) = 9% = 0.09

tenure ( t ) = 15 years

hence Final cost of investment ( A ) = P + Prt

A = 7000 + ( 7000 * 0.09 * 15 ) = $16450

Annual incomes

First year = $1100

2nd year = $1100 - $45 = $ 1055

3rd year = $1055 - $45 = $1010

4th year = $1010 - $45 = $965

5th year = $965 - $45 = $920

6th year = $920 - $45 = $875

7th year = $875 - $45 = $830

8th year = $830 - $45 = $785

9th year = $785 - $45 = $740

10th year = $740 - $45 = $695

11th year = $695 - $45 = $650

12th year = $650 - $45 = $605

13th year = $605 - $45 = $560

14th year = $560 - $45 = $515

15th year = $515 - $45 = $470

Total annual income = ∑ yearly incomes = $11775

It is not a good investment because  

∑ yearly incomes < Final cost of investment

i.e.  $11775  <  $16450

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