The reason compound interest earn you a higher APY on savings account is with compounding you earn interest on the money that has already earned interest.
With compound interest, interest is earned on the amount of money that has already earned an interest. On the other hand, with simple interest, interest is earned only on the principal.
Imagine that you deposit $100 in a savings account with an interest rate of 10% and annual compounding.
Value of the account in one year = 100 x (1.1) = 110
Value of the account in two years = 100 x (1.1)² = 121
Imagine that you deposit $100 in a savings account with an interest rate of 10% and simple interest.
Value of the account in one year = 100 + (100 x 0.1 x 1) = 110
Value of the account in two years = 100 + (100 x 0.1 x 2) = 120
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