**There’s a saying—money doesn’t grow on trees.**

You’ve heard it as a way to tell you that money is limited, you can’t just make it up out of nowhere. But what if I told you that math could help you make your money grow faster?

In past blogs I’ve discussed some lessons you can learn from Shark Tank, and also how mortgages work. The problem with mortgages, as I discussed, is that interest hurts you and you often have to pay wayyyyy (check out all those y’s!) more money than your original loan.

**But what if you could flip the script? What if you could start to make interest work to your benefit?**

Well you can, and it all comes from a little formula that helps to determine the Future Value of a Sinking Fund. Now we’re not talking about sinking ships here, we are talking about sinking money into an account that is already earning you interest.

If you make a payment (marked PMT below) at the end of each month into an account that is earning interest at a rate (i) compounded (m) times per year, your money will grow incredibly fast.

So let’s break that down because there is a lot going on here. The formula for the Future Value of a Sinking Fund is:

FV = PV(1 + i)^{n} + PMT (1 + i)^{n} – 1

**Woah, woah, woah. **How is anyone supposed to understand this formula? How do all these letters make my money grow faster? Well, allow me to explain. First let’s start with the terms in the formula (everything below is based on monthly interest compounding):

**PV =** Present Value, or the amount of money that is currently in an account.

**i =** the interest rate, as a decimal of course. Note: If this was a yearly interest rate, you would divide by 12 to figure out the monthly interest (we’re going to assume monthly compounding interest in all my examples).

**n= **number of compounds you want to calculate (or more simply put, the time)—if it was compounding monthly and you wanted to know how much you would have after a year, this would be 12. Two years would be 24, three would be 36, etc.

**PMT = **money that you will “sink” into the account every month

**So here’s an example:** Let’s say you deposit $100 per month into an account that now contains $1,000 and earns 6% interest per year compounded monthly. We want to see how much money will be in the account after 10 years

FV= 1000 (1+ .06/12)^{120} + 100 (1+ .06/12)^{120}-1

.06/12

So some things to point out before we move on. The 120 comes from 10 years x 12 months. The .06/12 comes from 6% YEARLY changed to MONTHLY

So here are the calculations broken down:

FV= 1000 (1+ .06/12)^{120} + 100 (1+ .06/12)^{120}-1

.06/12

FV = 1819.40 + $16387.93

FV= 18207.33

**So what started as $1,000 and adding $100 a month has now become over $18,000. Incredible!**

Now, my example is a little, we will say, optimistic, because you probably won’t find a bank that pays out such a huge interest rate. My example is just to show how quickly your savings could grow.

But is it a big difference to use a more real world rate? Let’s go with a more accurate example. I looked up Certificate of Deposit (CD) rates in Maryland, and found one that is 1.51% per year. Using that example, let’s make our calculations with the same present value ($1,000) and payments (100) over the same time:

FV= 1000 (1+ .0151/12)^{120} + 100 (1+ .0151/12)^{120}-1

.0151/12

FV = 1162.89 + $12944.60

FV = $14107.49

Even with a lower rate, we are still ending with over $14,000. That’s a lot of money to make by just putting in $100 a month. Without the interest rate we’d be looking at:

1000+ (100x120) = $13000

PV + (PMT x n)

Without doing anything, interest is working for us! So get out there and let interest be your best friend!

**Tip for Teachers:**

Use the examples from this blog as real world applications of math in your next math class, to help your students understand the ways in which mathematics is interwoven with our daily lives—and can help them succeed at business!

**About the Author**

Chris Brida is a mathematics teacher in Baltimore, MD. He currently teaches 9^{th} grade Algebra. Chris is a regular guest contributor to our blog, and we feel lucky to have him.

**A note on guest posts:** Our community blog is a place for educators from all walks of life to share opinions and exchange ideas. Simply because a post appears here does not necessarily mean we endorse the views presented therein. That being said, we'd love to hear what you think! Please post any questions or comments below, and we'll get right back.