Compound Interest Formula:
The future value of money is how much it will be worth at some time in the future. The future value formula shows how much an investment will be worth after compounding for so many years.
$$ F = P*(1 + r)^n $$The future value of the investment (F) is equal to the present value (P) multiplied by 1 plus the rate times the time. That sounds kind of complicated, so here's an example:
Bob invests $1000 today (P) and an interest rate of 5% (r). After 10 years (n), his investment will be worth:
$$ F = 1000*(1+.05)^{10} = 1,628.89 $$Make sure to convert the interest rate from a percentage (like 8%) to a decimal (like .08).
Continuously Compounded Interest:
Instead of having interest added each year, investments often have continously compounded interest. Basically, instead of having one lump sum payment every month or every year, the interest is applied constantly, but at an incredibly low rate each time.
The formula for continously compounded interest is:
$$ F = Pe^{rt} $$The future value (F) equals the present value (P) times e (Euler's Number) raised to the (rate * time) exponential. For example: Bob again invests $1000 today at an interest rate of 5%. After 10 years, his investment will be worth:
$$ F=1000*e^{.05*10} = 1,648.72 $$In this formula, you'll want to convert the percentage (5%) to a decimal (.05), but you do not need to add 1. The future value is slightly more than before, because each small piece of interest earns interest on itself during the year.
Here is a future value calculator that uses continously compounded interest:
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