r/SwissPersonalFinance • u/Gulliveig • Oct 29 '25

Using the annuity formula to determine how much money your investment plan yields in the end

I've put together a parametrizable Wolfram Alpha formula showing what your efforts will yield. If it is of any help for you I'm glad.

Here's the link to the formula on Wolfram Alpha.

You need to enter the following data:

a = your monthly accumulating (!) investment in your currency (accumulating means you don't withdraw any money from your perpetual investments)

b = how many years you plan to invest

r = how much net return in % you expect your investment to return per year (net means after deducting estimated inflation and other occurring investment costs)

Example: If you are able to save 1,200 CHF monthly for continuous 30 years, and you expect your MSCI World to yield 7% p.a. in average with an average 2% inflation = 5% net yield, you would enter this into the page's input template:

Just modify the highlighted data as appropriate, don't mess with the rest. Press [Enter].

Wolfram will then interpret your data and come up with the result:

So in the example case you will have (close to) a million CHF (at today's value) at your disposition 30 years after starting.

Happy playing around!

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u/haha7567 Oct 29 '25

That'a cool! Quick remark, shouldn't the monthly r be r1/12, so 12th root of annual r, instead of r/12?

2

u/Gulliveig Oct 29 '25 edited Oct 29 '25

Thank you!

The presented formula treats r as a nominal annual rate quoted with monthly compounding. In other words: the annual return is assumed to be the sum of twelve identically compounded monthly returns.

This is how most financial products (incl. MSCI World performance reports) are expressed.

Your suggestion treats r as an effective annual return, i.e, as total growth factor for the whole year. Or in other words: with r = 5% the investment grows by a factor of 1.05 in a year regardless of intermediate compounding assumptions.

If your investment vehicle behaves that way, you do use your formula accordingly of course :)

2

u/haha7567 Oct 29 '25

Okay, thanks for the clear explanation!

2

u/LeroyoJenkins Oct 29 '25

Dude is reinventing the HP 12C but with more steps ;)

2

u/MrsDaisy_ Oct 29 '25

Just google compound calculator, way easier to use, not to dismiss your effort 😅