  # Financial Literacy Lesson 5 – Compound Interest with Contributions

Today we’re playing with my compound interest contribution calculator that I made myself, you can’t find it anywhere else, which is why you should subscribe to our newsletter because you get this calculator for FREE with subscription.

Please check out our last video of how we calculate compound interest for principle. It will give you a brief understanding of how to use the calculator for simple calculations without contributions.

In today’s post, we’re going to show you how to calculate the future value of a series, which is compound interest plus contributions at intervals. If this is already going over your head, don’t worry, it’ll all be explained soon in the examples that follow.

## Compound Interest Contributions At the End of the Month Example

Here’s our scenario:

If an amount of \$5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, with additional deposits of \$100 per month (made at the end of each month). The value of the investment after 10 years can be calculated as follows…

Notice that 5% annual interest rate in a savings account DOES NOT exist, this is just an example.

You’re adding \$100 at the end of the month. So, let’s say it’s April right now, we deposit the \$100 at the end of April, so for the entire month of April, we miss the interest earned from April due to the contribution being made at the end of April. However, we will get the interest earned on the next month, May.

This is what we mean by additional deposits made at the end of the month.

The compound interest contributions formula a.k.a Future Value of a Series (DEPOSITS MADE END OF MONTH) is as follows:

FV = PMT × {[(1 + r/n)(nt) – 1] / (r/n)}

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

PMT = the monthly payment

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time (months, years, etc) the money is invested or borrowed for

FV = Future Value Of Series

This is more complicated than plain compound interest, once you add contributions, it just makes things stupid.

In our compound interest contributions formula, we are using PMT, which is the monthly payment (or contributions). In our example, it’s the \$100. n is the number of times that interest in compounded and this is usually monthly. Therefore, it’s usually 12 unless stated otherwise. t is the time the money is invested or borrowed for. Pretty standard.

I know what you’re thinking right now.

Why am I learning this? It’s too complex!

That’s why I made you the calculator! Use the calculator and plug in your numbers and your situation and it’ll return to you the final amount. That’s what we’re interested in anyways (Get the calculator here).

So with this formula our final amount is

FV = PMT × {[(1 + r/n)(nt) – 1] / (r/n)} 100 × {[(1 + 0.05/12)(12*10) – 1] / (0.05/12)}

Which is, \$15,528.23.

So our Future Value is \$15,528.23.

### Don’t Forget the Original Compound Interest For Principal

We still have to add the compound interest for the initial payment of \$5,000 because the initial payment earned interest throughout this time as well. So, using the formula:

P(1+r/n)(nt) 5000(1+0.05/12)(12*10)

Which comes out to \$8,235.05

So the total is \$15,528.23 + \$8,235.05 which equates to \$23,763.28.

## Compound Interest Contributions At the Beginning of the Month

Same example. Let’s copy and paste the scenario…

If an amount of \$5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, with additional deposits of \$100 per month (made at the START of each month). The value of the investment after 10 years can be calculated as follows…

In my month of April, instead of adding the contribution at the END, we add it at the START of April. It will earn the interest on the entire month of April. The formula requires a slight change, so let’s look at the formula first.

PMT × {[(1 + r/n)(nt) – 1] / (r/n)} × (1 + r/n)

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

PMT = the monthly payment

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time (months, years, etc) the money is invested or borrowed for

FV = Future Value Of Series

So, the only change was tacking on that × (1 + r/n) to the end of the Future Value of a Series (DEPOSITS MADE END OF MONTH) formula.

So, the example will give us:

FV = PMT × {[(1 + r/n)(nt) – 1] / (r/n)} × (1 + r/n) 100 × {[(1 + 0.05/12)(12*10) – 1] / (0.05/12)} × (1 + 0.05/12)

Or

\$15,592.93 for our Future Value (Deposits made START OF MONTH).

Don’t forget to add the compound interest for principal, which makes for:

\$15,592.93 + \$8,235.05 = \$23,827.98

The difference between contributing at the start and end of the month is:

\$23,827.98 – \$23,763.28 or \$64.70.

## Compound Interest plus Contributions Formula Reference

To be completely transparent, I got the formulas from this site. I read through their analysis and did the calculations and they made sense. So, I took their formula and leveraged it to make my own calculator (get it now), but it’s still my calculator!

That’s all for today’s post!

## Check out the accompanying “Financial Literacy Lesson 5 – Compound Interest with Contributions” Video Tutorial

If you enjoyed this post, please share!