< DICTIONARY

# Compound Interest

#### As an example, \$500 invested when a child is born and invested with 7% interest per year can multiply by 3.5 times to \$1,756 after 18 years or by 87 times to \$43,546 after 64 years without adding a single dollar to the investment thanks to the effects of compound interest. ## What is Compound Interest?

In simple words, compound interest means you earn money on your original investment and also on the interest that your money earned.

Compound interest has a snowball effect for your money.

It's like earning "interest on interest," which helps your money grow faster.

Over many years, these small additional earnings add up and helps your savings grow faster and faster.

This is different from simple interest.

Kids that learn about it at a young age get more time for compound interest to work its magic.

With simple interest, you earn extra money only on your original investment, and that's it. The interest you earned in the previous term doesn't earn any additional interest over time.

Compound interest plays an important role in building generational wealth.

The longer the time horizon, the more significant the compounding effect becomes.

Kids that learn about it at a young age get more time for compound interest to work its magic.

Thanks to the power of compound interest, the \$10,000 investment has ballooned to an astounding \$933,896!

On the flip side, compound interest can work against you if you're not careful.

Take credit card interest as an example.

If you don't pay your full credit card bill each month, you'll be charged interest on the remaining balance.

Then, in the next month, you'll be charged interest not only on your original balance but also on the interest from the previous month.

On the flip side, compound interest can work against you if you're not careful.

Over time, this can lead to large, snowballing debt.

## Compound Interest Formula

The compound interest formula is:

A = P (1 + r/n)^(n*t)

This formula helps in calculating the future value of an investment or loan, which includes the effect of compounding.

Where:

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

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

r = annual interest rate (in decimal)

n = number of times that interest is compounded per year

t = time the money is invested or borrowed for, in years.

This formula helps in calculating the future value of an investment or loan, which includes the effect of compounding.

Let's look at it again in simpler terms:

Future Money = Original Money x (1 + Interest Rate / Number of Times Interest is Added in a Year) ^ (Number of Times Interest is Added in a Year x Number of Years)

Don't worry if it looks a bit confusing!

The main thing to remember is this: the more times interest is added (like monthly or yearly), and the longer your money is invested, the bigger your future money will be.

Future Money = Original Money x (1 + Interest Rate / Number of Times Interest is Added in a Year) ^ (Number of Times Interest is Added in a Year x Number of Years)

Let's try it out with an example.

Imagine you've invested \$1,000 in a high yield savings account with an annual interest rate of 5% (or 0.05 in decimal form), compounded monthly.

You plan to keep this investment for 10 years.

So in this case:

P = \$1,000

r = 0.05

n = 12 (as the interest is compounded monthly)

t = 10

If we substitute these values into the formula, we get:

A = 1000 x (1 + 0.05/12)^(12 x 10)

Simplified, that comes out to:

A = 1000 x (1.00416)^120

When you calculate this, it results in A = \$1,647.01

This means, after 10 years, your investment will grow to \$1,647.01 with compound interest.

## Compound Interest Vs Simple Interest

Simple interest is straightforward.

It's the extra money you earn (or owe) only on your original investment (or loan).

It doesn't change over time.

Picture it this way: you put \$1,000 in a savings account that pays a 10% annual simple interest.

This means, at the end of the year, you'll earn \$100 in interest (10% of \$1,000).

The next year, you'll earn another \$100.

And the year after that, another \$100.

Simple interest doesn't change over time. Compound interest grows and grows as time goes by.

No matter how many years pass, you'll always earn \$100 each year with this simple interest rate.

Then there's compound interest, which is a bit like a snowball rolling down a hill and getting bigger.

Imagine if you put that same \$1,000 into a different account.

This time it grows with a 10% annual compound interest.

After the first year, you're in the same boat as before - you've earned \$100 and your total is \$1,100.

But in the second year, you're earning 10% not just on your initial \$1,000, but also on the \$100 interest you earned in the first year.

So, you get \$110 in interest for the second year, and your total increases to \$1,210.

This is the main difference between compound interest and simple interest.

As the years go by, the power of compounding becomes more and more apparent.

You earn interest on the previously earned interest, on top of your initial investment.

As the years go by, the power of compounding becomes more and more apparent.

After 20 years, the simple interest account would have grown to \$3,000 (\$1,000 original + \$100 x 20 years).

However, the compound interest account would be much larger - approximately \$6,727!

The next year, you'll earn around \$673 in interest.

That's almost 7 times the yearly interest you'd be getting with a simple interest rate.

And it doesn't stop there.

The magic of compound interest continues to work over longer periods.

An initial \$1,000 investment made when your child is born can grow and grow into a \$490,370 by the time they retire at 65!

That last year, the 10% interest is about \$44,500.

That's what we call magic.

## Teaching Kids About Compound Interest

It's never too early to start teaching our kids financial literacy.

Understanding the power of compound interest is an essential financial lesson.

It forms the basis of how money can grow over time and instills the habit of saving and investing.

It also warns from the dangers of taking on too much debt.

Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.

Typically, introducing the concept of compound interest can begin as early as age 7 or 8.

That's when kids start understanding the concept of time and patience.

By the time they reach their teenage years, they'll be ready for more detailed discussions and calculations.

Here are a few ways to teach your kids about compound interest:

### 1) The Penny Riddle

One great way to demonstrate the power of compound interest to kids is through 'The Penny Riddle'.

While the instant million seems like the better choice at first, it is actually the penny that becomes more valuable in the end - exceeding \$5 million after 30 days!

This tangible example vividly illustrates the magic of compound interest.

### 2) Einstein's Quote

Use Einstein's famous quote: "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."

Einstein is an iconic figure that children are often familiar with from a young age.

Using his quote provides a connection between something they're learning - compound interest - and someone they recognize as being extremely smart.

### 3) Real-Life Scenarios

As kids get older, real-world examples can be powerful tools.

If they have a savings account, show them how the interest on their savings compounds over time.

Open a UTMA account for your kids when they're young, then show them how their money has grown over the years when they're older.

If they receive an allowance or earn money, demonstrate how saving and reinvesting a part of their money can yield more in the future due to compound interest.

Remember, the key is to make the learning process enjoyable and relatable.

Once they grasp the concept of compound interest, they're already on their way to understanding the importance of saving and investing for the future.

## Compound Interest Examples

Let's take a look at a few examples from real life scenarios.

### 1) Investing in a Savings Account

Let's say you deposit \$5,000 into a savings account that earns 5% Annual Percentage Yield (APY), compounded monthly.

In the first month, the interest earned is about \$20.83 (\$5,000 * 0.05 / 12).

Your account balance at the end of the first month becomes \$5,020.83.

In the second month, you earn interest on \$5,020.83, not just your initial deposit of \$5,000.

The interest for the second month comes to about \$20.92 (\$5,020.83 * 0.05 / 12), making your balance at the end of month two \$5,041.75.

This process continues, and by the end of the year (12th month), your savings account balance has grown to approximately \$5,255.81.

The interest earned in that last month was \$21.81.

By the way, this is more than what you would have if the interest was calculated once at the end of the year (which would give you \$5,250).

This process, where the interest is added to the account balance every month (not just at the end of the year), is known as monthly compounding.

### 2) Investing in a Custodial Roth IRA for a Child

Suppose you invest \$10,000 in a Custodial Roth IRA for your child.

The money is invested in an S&P 500 index fund, which historically has returned an average of about 7% per year, after adjusting for inflation.

After the first year, with compounding, the investment grows to approximately \$10,700.

By the 10th year, the investment has more than doubled to around \$20,096.

After 30 years, the investment has grown significantly to approximately \$81,164.

Fast-forwarding to 65 years from the original investment, thanks to the power of compound interest, the \$10,000 investment has ballooned to an astounding \$933,896!

### 3) Paying Off Credit Card Debt

Now, let's consider a credit card balance of \$5,000 with an 18% annual interest rate.

If you make the minimum payment of \$100 each month, here's what happens:

In the first month, you pay \$100, reducing your balance to \$4,900. However, you're also charged interest for that month, which is about \$73.50 (\$4,900 * 0.18 / 12).

So, at the end of the first month, your new balance is \$4,973.50.

In the second month, you pay another \$100, but you're charged interest on \$4,873.50, which comes out to be approximately \$73.10.

Notice how you are paying interest on the balance with the added interest from the first month.

By the end of the 12th month, after making all your payments, your balance will have reduced to \$4,685.62.

The bad news is, you've paid \$1,200 over the year, but your balance has only reduced by \$314.37 because of the high interest rate compounding every month.

This shows how compounding can work against you when it comes to debt.

## Compound Interest FAQs

### What is compound interest in simple words?

It's when you earn money on your investment, and then earn even more money on the investment plus on the money you earned.

It's essentially interest on interest, which can cause wealth to grow at a rate that grows and grows over time.

### What is the formula for compound interest?

The compound interest formula is A = P (1 + r/n)^(n*t).

It's a math formula that tells you how much your savings will grow over time, based on the amount you save, the interest rate, and the number of years you save.

Put another way:

Future Money = Original Money x (1 + Interest Rate / Number of Times Interest is Added in a Year) ^ (Number of Times Interest is Added in a Year x Number of Years)

### What is the difference between simple interest and compound interest?

The main difference is that simple interest is calculated on only the principal amount, while compound interest is calculated on both the principal and any interest already earned.

As a result, compound interest allows money to grow faster over time.

### How can I get compound interest for my kid?

You can get compound interest for your kid by opening a savings account or an investment account in their name.

The money saved or invested will earn interest, and then that interest will earn more interest, growing their money over time.

The key is to start as early as possible, as compound interest needs time to work its magic.