10% increase on an item what would you spen over 100 years

[Guest]

If an item was say worth \$20 and you purchased it this year and next year it had gone up by 10% it would now be worth \$22.

If you bought this one at \$22 as well as the first one for \$20 you would have spent a total of \$42 dollars.

How would you calculate this 2 year example for 100 years?

So year 3 the item would be \$24.20 + 22 + 20 = Total spent \$66.20

[Guest]

It is a geometric series with first term 20, common ratio 1.1.
Because we have [tex]20 + 20*1.1+(20*1.1)*1.1 +((20*1.1)*1.1)*1.1 ... = 20 + 20*1.1 + 20*(1.1)^2+20.(1.1)^3[/tex]
Formula is [tex]20\frac{1-1.1^{100}}{1-1.1}[/tex]

Here is more:
https://www.math10.com/en/algebra/geome ... ssion.html