[Note: We have corrected a typographical error that showed “time” as a factor rather than an exponent.]
If you save $1,000 today, what will it be worth 30 years from now?
Luckily, you can skip the crystal ball and use a pretty simple formula to get an idea of what your future wealth will be.
The concept is called “future value,” and it’s one of the most powerful concepts in finance.
The future value formula comes in handy if you want to figure out what your savings account might be worth in 10 years, how high your rate of return needs to be to reach your goals, and even how much money you need to save each year to hit a retirement milestone.
The concept may seem intimidating, but I’ll walk you through some examples to show you how simple it can be. Let’s start with the formula:
FV = PV*(1 + i)ˆt
FV = future value of the investment
PV = present value of the investment
t = the number of compounding periods, and
i = the periodic interest rate, inflation rate or rate of return*
Let’s jump right into an example.
Calculate Future Value
Assume you have $5,000 in your savings account right now and your bank pays interest of 1.5% each year. Let’s use the future value formula to find out what your account will be worth in 40 years.
PV = $5,000
t = 40
i = 1.5%
Plugging those numbers into the formula, we get:
FV = $5,000*(1 + .015)ˆ40 = $9,070.09
In 40 years, your savings account will be worth $9,070.09.
Calculate the Rate You Need
Now consider this: By using just a little bit of algebra, you can rearrange the formula to solve for whatever variable you want. For example, if you’d rather find out what rate of return you need to reach a savings goal, you simply need to fill in the other parts of the formula and solve for i.
So, let’s say that you need to have $10,000 in your account two years from now, and you currently have $8,000. What rate of return do you need in order to reach your $10,000 goal?
The formula looks like this:
$10,000 = $8,000*(1 + i)ˆ2 = 0.118 = 11.8%
You need to find an investment with an 11.8% annual rate of return to meet your goal.
One More Adjustment Before You Go…
As you can see, the future value formula can give you a lot of insight into the direction your investments are heading. But there is one important thing to remember: Because purchasing power changes over time due to inflation, it’s very important that the rate of return (the i in the formula) accounts for it, too.
You can do this by using the “real” rate of return instead of the “nominal” rate of return. The “real” rate of return is calculated by subtracting the inflation rate from the rate of return.
For example, if you invest in a bond that pays 5% per year (that’s the nominal interest rate) you need to subtract the inflation rate (typically 2% or 3%) from the nominal interest rate to find the real interest rate. Thus, if you subtract 3% from the 5% nominal interest rate, you’ll use a real interest rate of 2% in your calculations.
The Investing Answer: Use future value to determine what you need to invest each year and what those investments need to return so that you can reach your goals. Luckily, there are plenty of ways to outsource the work. We have a handy tutorial called “How to Calculate Future Value Using Excel or a Financial Calculator” along with four amazing savings calculators that will give you plenty of insight into reaching your financial goals.