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

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  

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.

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

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.

$PV=\frac{A}{r}$

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

a)

$PV=\frac{4,350((1+0.06)^{15}-1) }{0.06(1+0.06)^{15} }$

$PV=\frac{6075,02814 }{0,143793492 }= 42.248,28$

b)

$PV=\frac{4,350((1+0.06)^{40}-1) }{0.06(1+0.06)^{40} }$

$PV=\frac{40392,87303 }{0,617143076 }= 65.451,39$

c)

$PV=\frac{4,350((1+0.06)^{75}-1) }{0.06(1+0.06)^{75} }$

$PV=\frac{339547,6054 }{4,743415247 }= 71.582,94$

d)

$PV=\frac{4,350}{0.06} =72,500$

Best of luck