Simple interest is interest calculated on the original principal, so the amount of interest added each period is fixed, for example, 5% of the original amount you put in each year. Compound interest, meanwhile, increases each period by a percentage of the current amount.
This doesn't sound like a big difference, but exponential growth is a powerful thing, and a bank account with compound interest can end up significantly richer than one with simple interest.
Let's deposit $\$5000$ into two accounts, both with 5% annual interest. Account $A$ has simple interest, and account $B$ has compound interest.
Account A's balance increases every year by $(0.05\times5000)=\$250$.
Meanwhile, account B's balance gets multiplied by $1.05$ every year.
After 50 years, account A will have a balance of $(5000+50(0.05\times5000))=\$17500$.
After 50 years, account B will have a balance of $\$5000(1.05)^{50}\approx\$57337$.
You can see here how compound interest is a lot more profitable than simple interest!
The compound interest formula is: $$ A = P(1 + r)^n $$ Where:
When converting interest rates to decimals, divide the percentage by 100. For example, 5% becomes 0.05
This might look familiar. This is because this is really just a geometric series where the common ratio is $1 + r$.
For example, if the compound interest rate is $5\%$, the common ratio the balance increases by each year is $1.05$.
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