96.3k views
5 votes
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

1 Answer

0 votes

Answer:

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

User Jsotola
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories