In order to predict how well your investments are going to do over the long-term, you need to know your current compound average growth rate (CAGR) — how well your investments have done in the past up to today — and then use that rate to estimate a future value of your investments.

But most of your investment account statements probably just show your average cost and your current market value. From those two numbers you can easily calculate your total growth since your purchase date, but that’s a hard number to extrapolate into the future. In order to figure out your current CAGR, you need to incorporate the current time period into the formula.

Total growth

First, if the cost of your investments is $10,000 and the market value today is $13,000, then how much has your growth been (as a percentage) over the investment period? To figure that out, you would use:

[ ( Present Value - Cost ) / Cost ] * 100%
[ ($13,000 - $10,000 ) / $10,000 ] * 100%
[ $3,000 / $10,000 ] * 100%
0.30 * 100%
= 30%

Current CAGR

But what if you want to find out your compound annual growth rate (CAGR) over a specific time period? More specifically, in order to estimate how well your investments will do over the long-term, you need to figure out your CAGR and then project that forward to come up with an estimate for a future value. For interest’s sake, let’s use the same dollar figures as above, but a total investment period of 2 years and 9 months.

How do you figure out a CAGR for those same dollar amounts, and that same growth, but over 2.75 years? The formula is:

{ [ ( Present Value / Cost ) ^ ^1/Period ] – 1 } * 100%

So, for $3,000 of growth on $10,000 over 2 years and 9 months, we would use:

{ [ ($13,000 / $10,000 ) ^ ^1/2.75 ] – 1 } * 100%
{ [ 1.3 ^ ^0.364 ] – 1 } * 100%
{ 1.10 – 1 } * 100%
0.10 * 100%
= 10%

Into the future

So now that we know our annual growth rate is 10% per annum, we can estimate what the future value of our investments will be assuming that the average rate stays the same. Of course, if the average rate changes, then so will our future value.

If our average annual rate is maintained 10%, how much will our $13,000 investment be worth in 7 years? We would use:

Present Value * ( 1 + CAGR ) ^ ^Period

So with our numbers, that gives us a future value of:

$13,000 * ( 1 + 0.10 ) ^ ⁷
$13,000 * 1.10 ^ ⁷
$13,000 * 1.949
= $25,333

Other uses: What rate do I need?

Another use of the formula for the current CAGR is to figure out the required average CAGR into the future in order to achieve a certain future value. For example, if we invest our $13,000 for another 10 years, what CAGR do we need to maintain in order to achieve a future value of $50,000 in that time period? We would use:

{ [ ( Future Value / Present Value ) ^ ^1/Period ] – 1 } * 100%

And with our numbers:

{ [ ($50,000 / $13,000 ) ^ ^1/10 ] – 1 } * 100%
{ [ 3.85 ^ ^0.10 ] – 1 } * 100%
{ 1.14 – 1 } * 100%
0.14 * 100%
= 14%

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