Is compound growth simply the growth rate multiplied by itself? In other words, if my $100 stock grows by 1% a day, it will only rise by $1 a day in the beginning. However, if it eventually hits $1,000, my stock will rise by $10 per day at that same 1% growth rate. Given that compound growth is dependent on growth rate rather than absolute unit growth, would it imply exponential growth as well?
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After the first year, $100 increases to $110 at a 10% compound annual growth rate (CAGR). In the second year, the initial $100 grows by an additional $10 PLUS the $10 from the previous year grows by $1, giving you a gain of $11.
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The interest accrued on top of your initial investment and any prior interest is known as compound interest. It gradually increases as a result of the beginning number growing.
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Compound growth is exponential because it depends on the growth rate rather than the absolute increase. With a 1% daily growth rate, the growth speeds up as the initial investment’s value rises. 
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To put it simply, compounding is the process of earning growth on growth. In a year, if I deposit $1000 into an account with a 10% annual percentage yield, I will have $1100. In two years, I will be worth $1210. The compounding is that additional $10. The account would increase by $100 annually if it were simple interest, where you would just be paid interest on your base.
You can use one of the billion online calculators to find the answer to your inquiry about how to get $X in 25 years.
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Absolutely, and thanks for your response. Honestly, one of the main reasons I posted is because I am not entirely sure I’m using those calculators correctly.