Compound interest by itself is pretty dang amazing. If you want to turbo charge your money growth, as you should, then compound interest with regular contributions is the way to go. In this post we will look at how to calculate the future value of an investment with periodic compounding and regular savings contributions.
Compound Interest with Monthly Contributions
Calculating interest with regular monthly contributions is essential for planning and achieving your goals. This is a very powerful calculation that looks a little scary. But, like they always say, with great power comes great complexity, or something like that.
Contributions are the money out of your pocket that you are investing or saving. By consistently doing this, you will take the power of compound interest and give it a shot of super high-powered steroids. Also, by engaging in consistent periodic contributions, you are taking advantage of dollar cost averaging (DCA),
Formula for Regular Monthly Contributions
The formula to calculate the future value of compound interest with regular monthly contributions is:
A = P * (1 + r / n)nt + C * [((1 + r / n)(nt) – 1) / r / n]
OMG and WTF come to mind when you lay your eyes on this foul creature for the first time. But wait, look again and you will see this isn’t so bad after all. If you have read about how to calculate compound interest, you already know over half of this calculation.
Let’s take a closer look and define the new pieces of the puzzle.
A = Amount – future value, sometimes denoted by FV
RC = Regular Contributions – sometimes denoted as PMC or Periodic Monthly Contributions
P = Principal – investment amount
r = Interest rate as a decimal
n = Number of compounding periods
t = Number of years to compound over
C = Contribution amount
Understanding the Formula
There is a lot to take in with this formula. This is actually two formulas in one, and the way that I tackle this is to break it up. Looking at the calculation, the plus between compound interest and the monthly contribution is a logical place to separate them. Because of how operators work this addition will be the last thing that is performed.
The first part is just compound interest: A = P * (1 + r / n)(nt)
The second part of the calculation is the monthly contribution over the same number of compounding periods and years to compound: RC = C * [((1 + r / n)(nt) – 1) / r / n]. Here, I used RC to express Regular Contribution.
Now the reason for the – 1 is that you are not compounding on the original investment but the contributions only.
Examples
Let’s take a look at the same $10,000 investment at 8% interest compounded monthly for 6 years from before and adding in a $100 contribution each month.
From compound interest you earned $6,135.02. And on your contributions you earned another $2002.53. That $8,137.55 is money that you didn’t have to work for.
Here’s another example and only increasing the monthly contribution to $200
As expected, the interest you gained on monthly contributions doubled to match the increase. This is a fun calculation to play with and is a great planning tool. If you need to save money for a goal and you can find an interest bearing account, you can easily figure out how long it will take to reach your goal. Also, you can figure out ways to shorten the time to reach said goal. Even a $5 increase can have major impact to the time frame.
I like to break this equation up so I can see the compound interest earned as well as interest earned on the regular contributions side-by-side. It also makes it easier to work.