Sum of 10 years of compound interest on new principle each year with increasing rate

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I'm trying to calculate 10 years of compound interest on a principle. The difficulty lies in the fact that the principle needs to be added to the compounded interest each year, and each year the interest rate needs to increase by 5%.

The best way I can explain it is with a formula, which would go something like this:

A = (P * (1 + 0.05)) + (P * ((1 + 0.05) ^ 2) ...

And so on up until 10. I don't want to write it manually because it doesn't suit the case. How can I write an expression that will output only the result after 10 (or x) amount of years?