# Annuity Equation isolating n value HELP!

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1. May 4, 2008

### LordofDirT

Annuity Equation "isolating n value" HELP!

$$R =\frac{Pi(1+i)^n}{(1+i)^n-1}$$

1. I need to solve for n.
• n = number of years
• P = Investment
• R = Yearly Savings
• i = interest rate

3. My Attempt:

$$R =\frac{Pi(1+i)^n}{(1+i)^n-1}\rightarrow -1 \cdot R = \frac{Pi(1+i)^n}{(1+i)^n} \cdot -1$$

Once I get here I'm left with:

$$-R =\frac{Pi(1+i)^n}{(1+i)^n}$$

It seems like the quantities of $$(1+i)^n$$ cancel so I'm left with:

$$R = Pi$$

I know this isn't correct, and I've tried it many other ways with no luck.

Any help would be greatly appreciated!

Last edited: May 4, 2008
2. May 4, 2008

### tiny-tim

Welcome to PF!

Hi LordofDirT ! Welcome to PF!

(nice LaTeX, by the way … I think I'll just copy-and-paste it! )

Hint: $$\frac{(1+i)^n}{(1+i)^n-1}\,=\,1\,+\,\frac{1}{(1+i)^n-1}$$

3. May 5, 2008

### HallsofIvy

Staff Emeritus
I would be inclined to simplify at first: let 1+ i= u. Then the equation is
$$R= \frac{Piu^n}{u^n-1}$$
then rather than use tiny-tim's method (which is perfectly good) I would multiply on both sides by un- 1:
$$Ru^n- R= Pi u^n$$
isolate the un term:
$$Ru^n- Pi u^n= (R- Pi)u^n= R[/itex] [tex]u^n= \frac{R}{R- Pi}[/itex] to solve for n, you will now have to take a logarithm of both sides. (Don't forget to put 1+ i back in for u in the answer.) 4. May 5, 2008 ### LordofDirT the logarithm So to isolate the n variable in [tex]u^n= \frac{R}{R- Pi}$$

would i have to take the logarithm base "u" on both sides? Or will any logarithm work?

5. May 6, 2008

### tiny-tim

Hi LordofDirT!

Yes … n = (logR - log(R - pi))/logu, for any base of log.

btw, the reason I suggested my way (instead of HallsofIvy's, which is fine) was to get (1+i)^n just once in the equation … I reckon I'm quite likely to make mistakes, and that lessens the possiblity slightly!

6. Mar 30, 2009

### gardzrecah

Re: Annuity Equation "isolating i value" HELP!

hi everybody!

P = the principal = (63,000.00)
R = the amortized payment = (2750.00)
n = the Terms = (36 Months)

P = R((1-(1/(1+i)power of n))/i)

please i really need help to solve for i value....

thanks,.......

7. Mar 30, 2009

### tiny-tim

Welcome to PF!

Hi gardzrecah ! Welcome to PF!

(btw, it's always better to start a new thread … more people will see it)

(and try using the X2 tag just above the Reply box )

Show us what you've tried, and where you're stuck, and then we'll know how to help!