Question

If an amount of $100 in a savings account increases by 10% then increases by 10% again is that the same as increasing by 20

Answer 1

No, it's not.
increasing by a percentage means (1+percentage)
$100 * (1+0.1) = $110

$110 * (1.1) = $121

However, $110 * 1.2 = $132