Question

Algebrea, solve for I. Please show me all the steps?
PV = FV/(1 + I)^N

Answer 1

\[PV=FV(1+L)^n\] like that?

Answer 2

the letter I (eye)
The answer is I =(fv/pv) ^1/N -1..... but I am getting stuck after I cross multiply

Answer 3

ok ok don't do that
divide by \(FV\) first and get
\[\frac{P}{F}=(1+I)^n\]

Answer 4

then take the nth root to get
\[1+I=\sqrt[n]{\frac{P}{F}}\]

Answer 5

what happened to the latex lol

Answer 6

then subtract 1

Answer 7

\[\begin{align*}PV&=\frac{FV}{(1+I)^N}\\
(1+I)^N&=\frac{FV}{PV}\\
\ln(1+I)^N&=\ln\frac{FV}{PV}\\
N\ln(1+I)&=\ln\frac{FV}{PV}\\
\ln(1+I)&=\frac{1}{N}\ln\frac{FV}{PV}\\
\ln(1+I)&=\ln\left(\frac{FV}{PV}\right)^{1/N}\\
e^{\ln(1+I)}&=e^{\ln\left(\frac{FV}{PV}\right)^{1/N}}\\
1+I&=\left(\frac{FV}{PV}\right)^{1/N}\\
I&=\cdots
\end{align*}\]

Answer 8

if you prefer you can write
\[\sqrt[n]{1+I}=(1+I)^{\frac{1}{n}}\]

Answer 9

@SithsAndGiggles
at what point to you cancel the \(V\) ?

Answer 10

@satellite73 I took \(PV\) and \(FV\) to stand for present/future value.

Answer 11

oooh ok
one term i see
now i have a second question
why take the log and then exponentiate?

Answer 12

Yeah, I was gonna say your method was quicker... Oh well, another way to get the same result.

Answer 13

\[x^2=25\]
\[\ln(x^2)=\ln(25)\]
\[2\ln(x)=\ln(25)\]
...

Answer 14

I suppose this way you get rid of the negative root...

Answer 15

oooh i see

Answer 16

at least you didn't write "present value over future value" is "present over future" like i did lol

Answer 17

the instructor got the answer without using steps 3 - 5

Answer 18

@Iron, right, refer to satellite's steps. My method is a bit roundabout.

Answer 19

what is the nth root?

Answer 20

Given something like
\[x^n=10\]
you'd solve for \(x\) by taking the nth root of both sides:
\[\left(x^n\right)^{1/n}=10^{1/n}\\
x=10^{1/n}\]

Answer 21

So in the second step,
\[(1+I)^N=\frac{FV}{PV}\]
taking the nth root of both sides gives you
\[\left((1+I)^N\right)^{1/N}=\left(\frac{FV}{PV}\right)^{1/N}\\
1+I=\left(\frac{FV}{PV}\right)^{1/N}\]

Answer 22

i'm dumb. i still don't get it

Answer 23

For instance, when you solve the equation \(x^2=4\), how do you go about it?

Answer 24

to be honest i dont remember