Answer to Question #251929 in Microeconomics for queen

Question

Anna is thinking about making an improvement to her home. This modification will cost $10,000, but it will also increase the value of the home by $10,000 when Anna plans to sell it in 10 years. The market interest rate is 10%. 

a. What is the present value of the increased value of the home due to the improvement? 

b. What is the minimum amount at which Anna must personally value the improvement to be willing to go through with it? 

Answer 1

Solution:

a.). PV = FV (1 + r)^-n

Where: PV = Present Value

            FV = Future Value = 10,000

             r = Market interest rate = 10%

            n = Number of periods = 10yrs

PV = 10,000 (1 + 0.1)^-10

PV = 10,000$\times$0.3855432894 = $\$$3,855.43

The present value of the increased value of the home due to the improvement = $\$$3,855.43

 

b.). FV = PV (1 + r)ⁿ

Where: PV = Present Value = 10,000

            FV = Future Value =

             r = Market interest rate = 10%

            n = Number of periods = 10yrs

FV = 10,000 (1 + 0.1)¹⁰

PV = 10,000$\times$2.5937424601 = $\$$25,937.42

The minimum amount at which Anna must personally value the improvement to be willing to go through with it = $\$$25,937.42