# Financial Mathematics - Annuities

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1. Jul 29, 2009

### oooobs

http://www.intmath.com/Money-Math/annuity_6.gif [Broken]

Above is the annuities formula (change the - to a + as i am not using it for loans) used to calculate the amount of money accumulated over a period of time with compounding interest, with a monthly input of $W. the first part is an example of a Geometric Sequence i believe. P(1+r)^n I would like to find out how this formula would be altered if my input (W) was becoming greater by approx 3% p.a ? any help is greatly appreciated!! Thanks heaps! ~James Radford-Voss Last edited by a moderator: May 4, 2017 2. Jul 29, 2009 ### Mentallic I haven't had the benefit of studying annuities or even using this or similar formulas for that fact, so I don't know precisely what the formula represents. However, I'll throw in an idea to see if it helps. Since your$W is increasing by 3%/annum, couldn't we use another geometric sequence to express this?
So maybe (emphasis on the maybe), the W should be substituted with, say:

$$W(1+\frac{A}{100})^{m}$$

where A is the increase in percentage (3 in this case)
m is the frequency of increase (per annum, hence, 1 in this case)

This is just a guess, so don't take my word for it, and be very skeptical when attempting to consider its legitimacy

3. Jul 29, 2009

### HallsofIvy

Staff Emeritus
Then you would replace W by 1.03W so your formula becomes
$$B= P(1+ r)^n+ 1.03W\frac{(1+r)^n-1}{r}$$
$$= P(1+ r)^n+ W\frac{(1+r)^n-1}{r}+ 0.03W\frac{(1+r)^n-1}{r}$$

and the increase is that
$$0.03W\frac{(1+r)^n-1}{r}$$.

Last edited by a moderator: May 4, 2017