Compound Interest

1. Power of Compounding Interest

You’ve learned a little about compounding interest in a previous lesson, but let’s dig a little deeper and see how it works. Compounding interest is often referred to as the eighth wonder of the world. It’s the process where the interest earned on an investment earns additional interest over time. While it may sound like just another financial term, its impact is transformative—and it’s something anyone can take advantage of.

hint

Interest can be your best friend or your worst enemy. When it’s working for you, like with savings or investments, it helps your money grow exponentially. But when it’s working against you, like with credit card debt, it can make balances balloon fast. Knowing the difference is the key to staying in control.

Remember our previous explanation:

Think of compounding interest like planting a tree. At first, the growth seems small—a sapling with just a few leaves. But as time goes on, the tree grows bigger and starts producing seeds. Those seeds grow into new trees, and soon, you have a forest. Similarly, compounding allows your money to grow exponentially over time.

The magic of compound interest is that it grows your money faster and faster as time goes on. Why? Because you’re not just earning interest on the original amount you invested (your principal)—you’re also earning interest on the interest from previous years. It’s like a snowball rolling down a hill. At first, it’s small and slow, but as it rolls, it picks up speed and size.

EXAMPLE

Suppose you invest $1,000 at an annual interest rate of 5%, compounded yearly. Here’s how your investment grows over 5 years:

• Year 1: 1,000 × (1 + 0.05) = $1,050
• Year 2: 1,050 × (1 + 0.05) = $1,102.50
• Year 3: 1,102.50 × (1 + 0.05) = $1,157.63
• Year 4: 1,157.63 × (1 + 0.05) = $1,215.51
• Year 5: 1,215.51 × (1 + 0.05) = $1,276.28

hint

Wait, what’s that “1” for?
In the equation 1+0.05, here’s what’s happening in simple terms:

• The 1 represents the original amount of money you invested—you’re keeping that money intact.
• The 0.05 represents the 5% interest you’re earning on your investment that year.

When you add them together, you get 1.05. This means that for every $1 you invest, you end up with $1.05 after earning 5% interest for the year.

So, when you multiply your current balance by 1.05, you’re increasing it to include both your original money (the 1) and the extra interest earned (the 0.05). This process repeats each year, and the fun part is that you’re earning interest not just on your original amount, but also on the interest from previous years—that’s what makes your money grow faster over time.

At first, it seems slow, but by Year 5, the snowball effect is in full swing. Over decades, this effect becomes staggering, which is why starting early matters so much.

Imagine starting with just $100 a month in your 20s. By retirement, compounding can turn your modest savings into hundreds of thousands of dollars. This isn’t magic—it’s math, and it’s accessible to everyone.

See below how saving $100 a month starting at age 25 with a 9% interest rate compounds over 20 years ($100 a month = $1,200 in deposits a year).

You would have contributed just $24,000 over 20 years by contributing $100 a month and have a total of $66,917. You made $42,917 on your deposited money. This is the power of compounding interest.

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The Rule of 72 is an easy way to figure out how long it will take for your money to double with a steady interest rate without doing the compound interest calculation. Just divide 72 by the annual interest rate. For example, if you earn 6% interest, it will take 72 ÷ 6 = 12 years to double your money.

You can use this rule to quickly compare different investments or see how interest rates affect your savings over time. It’s a simple trick to understand how your money can grow.

try it

Try it yourself! Select the “+” button to see if you are correct.

Calculate how much a one-time deposit of $2,000 would grow in 10 years at a 6% annual interest rate, compounded yearly.

Answer:

Year 1: 2,000.00 × (1 + 0.06) = $2,120.00
Year 2: 2,120.00 × (1 + 0.06) = $2,247.20
Year 3: 2,247.20 × (1 + 0.06) = $2,382.03
Year 4: 2,382.03 × (1 + 0.06) = $2,524.95
Year 5: 2,524.95 × (1 + 0.06) = $2,676.45
Year 6: 2,676.45 × (1 + 0.06) = $2,837.04
Year 7: 2,837.04 × (1 + 0.06) = $3,007.26
Year 8: 3,007.26 × (1 + 0.06) = $3,187.70
Year 9: 3,187.70 × (1 + 0.06) = $3,378.96
Year 10: 3,378.96 × (1 + 0.06) = $3,581.70

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Let’s explore how compounding works over a shorter period. Imagine you invest a one-time deposit of $5,000 at an annual interest rate of 8%, compounded yearly.

Calculate how much your investment would grow over 3 years. Select the “+” button to see if you are correct.

• Year 1: 5,000 × (1 + 0.08) = $5,400.00
• Year 2: 5,400 × (1 + 0.08) = $5,832.00
• Year 3: 5,832 × (1 + 0.08) = $6,298.56

In just 3 years, your $5,000 grows to $6,298.56, earning you $1,298.56 without lifting a finger. The growth accelerates each year because you’re earning interest on both your original $5,000 and the interest that was added in previous years.

Even in a short time, compounding demonstrates its power. If you leave your investment untouched for longer—like 10 or 20 years—the growth becomes exponential. This is why starting early and being consistent with your investments are so important for building wealth over time.

Now that we’ve talked about the power of compound interest, let’s examine the negative impacts of compound interest related to debt.

terms to know

Compound Interest

The interest you earn on the amount deposited into your account and on the interest you already received.

Interest

The cost of borrowing money or the reward for saving money, usually expressed as a percentage of the amount.

Principal

The original amount of money borrowed, invested, or loaned before any interest or earnings are added.

Snowball Effect

When your money grows through compounding by earning interest on both your original deposit and interest on the interest.

2. Compound Interest and Debt

While compound interest can work wonders for growing your savings and investments, it can also work against you in situations like credit card debt. When you owe money, compounding interest means you’re not only paying interest on the original amount you borrowed but also on the interest that has been added to your balance. This can cause debt to spiral out of control quickly if you’re not careful.

did you know

So far, we’ve focused on annual compounding, but interest can also be compounded daily, monthly, or at other intervals. The frequency of compounding is important because it directly impacts how quickly your money grows—or how quickly debt can increase.

Compounding means that interest is added to the balance, and future interest is calculated on that new total. The more frequently this happens, the faster the growth. For example, interest compounded daily or monthly adds up faster than interest compounded annually.

Here’s how this plays out with a simple example: Imagine you invest $1,000 at a 5% interest rate over 1 year:

• Annually: Interest is added once at the end of the year, so you earn $50, making your total $1,050.
• Monthly: Interest is added 12 times, slightly increasing your balance each month. By the end of the year, you’d have around $1,051.16.
• Daily: Interest is added 365 times throughout the year, allowing it to grow even faster. By the end of the year, you’d have about $1,051.27.

While the difference may seem small over 1 year, the gap grows significantly over time, especially for long-term investments or loans.

When evaluating financial options like credit cards, loans, or savings accounts, always check how often interest is compounded. For savings and investments, more frequent compounding works in your favor. However, with debt, it can make balances grow quickly if you don’t pay off the principal.

Most credit cards charge compound interest on your balance if you don’t pay it off in full each month. For example, if your credit card has an annual interest rate of 20% (a typical rate) and you only make the minimum payment, the unpaid balance keeps growing as interest compounds daily or monthly.

EXAMPLE

Imagine you have a credit card balance of $5,000 with a 20% annual interest rate, compounded monthly, and you only pay the minimum payment of $100 per month.

Here’s what happens:

1. Month 1:

a. Starting balance: $5,000

b. Interest added: 5,000 × 20% (0.20) = 1,000 then divide by 12 months: 1,000 ÷ 12 = 83.33, or $83.33 of interest added this month

c. After paying $100 minimum, new balance: $4,983.33 (5,000 + 83.33 − 100 = $4,983.33)

2. Month 2:

a. Starting balance: $4,983.33

b. Interest added: 4,983.33 × 20% (0.20) = 996.67 then divide by 12 months: 996.67 ÷ 12 = 83.06, or $83.06 of interest added this month

c. After paying $100 minimum, the new balance is 4,966.39 (4,983.33 + 83.06 − 100 = $4,966.39)

3. Month 3:

a. Starting balance: $4,966.39

b. Interest added: 4,966.39 × 20% (0.20) = 993.28 then divide by 12 months: 993.28 ÷ 12 = 82.77, or $82.77 of interest added this month

c. After paying $100 minimum, the new balance is $4,949.16 (4,966.39 + 82.77 − 100 = $4,949.16)

After making 12 minimum payments (a total of $1,200), you’d still owe $4,780.61, and nearly $750 of your payments would have gone just to interest! If you keep making minimum payments, it could take years to pay off the balance—and you’d pay thousands of dollars in extra interest.

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Your turn! Imagine you owe $5,000 on a credit card with an 18% annual interest rate, compounded monthly, and you don’t make any payments to reduce the balance.

Calculate how the debt grows month by month over 4 months. Select the “+” button to see if you are correct.

1. Month 1:

a. Starting balance: $5,000

b. Interest added: 5,000 × 18% (0.18) = 900 then divide by 12 months: 900 ÷ 12 = 75, or $75 of interest added this month

c. New balance: $5,075.00 (5,000 + 75 = $5,075.00)

2. Month 2:

a. Starting balance: $5,075.00

b. Interest added: 5,075 × 18% (0.18) = 913.5 then divide by 12 months: 913.5 ÷ 12 = 76.13, or $76.13 of interest added this month

c. New balance: $5,151.13 (5,075 + 76.13 = $5,151.13)

3. Month 3:

a. Starting balance: $5,151.13

b. Interest added: 5,151.13 × 20% (0.18) = 927.20 then divide by 12 months: 927.20 ÷ 12 = 77.27, or $77.27 of interest added this month

c. New balance: $5,228.40 (5,151.13 + 77.27 = $5,228.40)

4. Month 4:

a. Starting balance: $5,228.40

b. Interest added: 5,228.40 × 20% (0.18) = 941.11 then divide by 12 months: 941.11 ÷ 12 = 78.43, or $78.43 of interest added this month

c. New balance: $5,306.83 (5,228.40 + 78.43 = $5,306.83)

In just 4 months, your balance grows from $5,000 to $5,306.83, adding over $300 in interest.

Many people fall into this trap because they don’t realize how quickly interest can compound. If you’re carrying a balance and only making minimum payments, you’re essentially working for your credit card company—they’re profiting off of you with compounding interest, just like you profit when it works in your favor with savings and investments.

Here are some suggestions to keep your debt from compounding negatively:

1. Pay more than the minimum. Paying even a little extra can drastically reduce the total interest you pay and help you pay off the balance faster.
2. Take advantage of any credit card offers with lower interest rates, like a 0% introductory rate. This will help more of your monthly payments go to paying off debt.