Question

A couple is deciding to invest in the laundromat business. There are two laundromat stores available for sale. They can only afford to buy one of them.

    The annual flow of income from each of the available laundromats is given below:

Laundromat 1: I’(t) = dI(t)/dt = 9000e^(.04t)

Laundromat 2: I’(t) = dI(t)/dt = 12500

The couple has decided to use the Present Value of each of the Laundromats after 8 years, at an annual interest rate of 10%, to compare the value of both investments.

They will buy the Laundromat with the highest Present Value.

1. Find the Present Value of each Laundromat

2. Which Laundromat should the couple buy? Explain.

         Hint: PV(t) = Definite ∫ I’(t)e^(-rt)dt, taken between ( a<t<b)

          Here a=0; b=8

                   r = 10%/100 = .10

Answer 1

Step 1)

we have,

we know that,

we have a = 0, b = 8 and r = 10% = 0.10

Hence,

rounding to two decimal places we can say that,

Step 2)

we have,

we know that,

we have a = 0, b = 8 and r = 10% = 0.10

Hence,

rounding to the two decimal places we can say that,

Step 3)

we can see that PV is larger if I'(t) = 12500 than the PV if I'(t) = 9000e^0.04t

Hence we can say that couple should buy Laundromat with I'(t) = 12500 that is Laundromat 2