Respuesta :
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.
[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]
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.
[tex]PV=\frac{A}{r}[/tex]
Now, let´s see how to solve all this step by step.
a)
[tex]PV=\frac{4,350((1+0.06)^{15}-1) }{0.06(1+0.06)^{15} }[/tex]
[tex]PV=\frac{6075,02814 }{0,143793492 }= 42.248,28[/tex]
b)
[tex]PV=\frac{4,350((1+0.06)^{40}-1) }{0.06(1+0.06)^{40} }[/tex]
[tex]PV=\frac{40392,87303 }{0,617143076 }= 65.451,39[/tex]
c)
[tex]PV=\frac{4,350((1+0.06)^{75}-1) }{0.06(1+0.06)^{75} }[/tex]
[tex]PV=\frac{339547,6054 }{4,743415247 }= 71.582,94[/tex]
d)
[tex]PV=\frac{4,350}{0.06} =72,500[/tex]
Best of luck
