Financial Mathematics - Annuities

[oooobs]

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

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

 

[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

 

[HallsofIvy]

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

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

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
$$0.03W\frac{(1+r)^n-1}{r}$$.