# Thread: Rearranging Annuitie formula to find R

1. ## Rearranging Annuitie formula to find R

Hey everyone I need help really badly.
I have a formula that looks like this
A=PR^n + Q(R^n-1)/R-1

But i need to rearrange it to make R the subject. Ive spent hours trying to work it out but i just can't do it. I need it for my maths assignment due tommorow so quick help would be very much appreciated.

Thanks!

2. Is it $A = PR^n + \frac{Q(R^{n}-1)}{R-1}$ or $A = PR^n + \frac{Q(R^{n}-1)}{R}-1$?

3. yeah thats the exact same equation I have, but I'm having trouble rearranging it to find R.

4. which one is it?

5. Oh sorry i didnt read it properly. Anyway its the first one.

6. $R^{n} = \frac{A}{P} - \frac{Q}{P}$

$R = \sqrt[n]{\frac{A}{P} - \frac{Q}{P}}$

This is how I did it:

We know that $A = PR^n + \frac{Q(R^n-1)}{R-1}$. Now $\frac{R^{n}-1}{R-1} = R^{n-1} + R^{n-2} + \ldots + 1$ which is a geometric series. So its sum is $\frac{1}{1-R}$.

Then $A = PR^{n} + Q \left(\frac{1}{1-R} \right )$

So $A = \frac{PR^{n}(1-R) +Q}{1-R}$ or $A(1-R) = PR^{n}(1-R) + Q$.

Then $\frac{A}{P}(1-R) = R^{n}(1-R) + \frac{Q}{P}$.

Then $\frac{A}{P} - \frac{Q}{P} = R^{n}$ and so $R = \sqrt[n]{\frac{A-Q}{P}}$

7. Thankyou so much!

8. This may be the beer talking but I don’t think that

is the solution to R in .

With P=100, R=1.05, n=11, and Q=50,

≈ 881.37.

But ≈ 1.21.