Present Value and Future Value

Present Value and Future Value

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

Where:

F = the initial investment

P = Present Value

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 compounding interest

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 continuously compounded interest:

Enter the initial amount (P), the interest rate (as a percentage, like 5 for 5%), the number of years invested, and click Compute to see the future value.

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