# Annuity Equation isolating n value HELP

• LordofDirT

#### 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:
Welcome to PF!

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

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

Hint: $$\frac{(1+i)^n}{(1+i)^n-1}\,=\,1\,+\,\frac{1}{(1+i)^n-1}$$ 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:
$$Ru^n- Pi u^n= (R- Pi)u^n= R[/itex] [tex]u^n= \frac{R}{R- Pi}[/itex] to solve for n, you will now have to take a logarithm of both sides. (Don't forget to put 1+ i back in for u in the answer.) the logarithm So to isolate the n variable in [tex]u^n= \frac{R}{R- Pi}$$

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

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! 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,...

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! 