Question

An investment offers $4,350 per year for 15 years, with the first payment occurring one year from now. a. If the required return is 6 percent, what is the value of the investment? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What would the value be if the payments occurred for 40 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What would the value be if the payments occurred for 75 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.1

Answer 1

Ans.

a) The value of the invesment of an annuity of $4,350, at 6% for 15 years is $42.248,28

b) If it was for 40 years, the value of the investment would be: $65.451,39

c) If it was for 75 years, the value of the investment would be: $71.582,94

d) If it was forever, the value of the investment would be: $72.500

Step-by-step explanation:

Hi, all we have to do is solve for "PV" the following equation for all the conditions of the problem, here is the equation.

`PresentValue=(A((1+r)^(n)-1) )/(r(1+r)^(n) )`

Where:

A= Annuity or yearly payment ($4,350)

r = require rate of return, in our case 0.06

n= periods to pay

This equation can be used with all the questions of the problem but d) which requires that we use the following equation.

`PV=(A)/(r)`

Now, let´s see how to solve all this step by step.

a)

`PV=(4,350((1+0.06)^(15)-1) )/(0.06(1+0.06)^(15) )`

`PV=(6075,02814 )/(0,143793492 )= 42.248,28`

b)

`PV=(4,350((1+0.06)^(40)-1) )/(0.06(1+0.06)^(40) )`

`PV=(40392,87303 )/(0,617143076 )= 65.451,39`

c)

`PV=(4,350((1+0.06)^(75)-1) )/(0.06(1+0.06)^(75) )`

`PV=(339547,6054 )/(4,743415247 )= 71.582,94`

d)

`PV=(4,350)/(0.06) =72,500`

Best of luck