Guide to Compound Interest: The Miracle Of Compound Returns

If you’ve heard anything about saving and investing, you’ll have heard about “the power of compound interest!” But how does compound interest work, and how can you make it work for you?

Here’s what you need to know.

What is compound interest?

Compound interest is earning interest from your savings and from the interest you earned before. People who already have money find it easier to get more money just by leaving their savings to grow. That’s the power of compound interest.

How does compound interest work?

When you save or invest money, you earn interest on your capital. The second year you earn interest on both your original capital and the interest from the first year. In the third year, you earn interest on your capital and the first two years’ interest. 

You get the picture. The concept of earning interest on your interest is the miracle of compounding.

It’s very much like a snowball effect. As your capital rolls down the hill, it becomes bigger and bigger. Even if you start with a small snowball, given enough time, you can end up with a gigantic one.

Simple interest vs. compound interest

Simple interest and compound interest are similar but have some slight differences.

If you lend someone £100 at 10% interest, they’ll pay you back £110 – that’s the original £100, which we call the principal, plus £10 interest. You could keep lending them the same £100 and earning £10 each time. After 10 loans, you’d have the original £100 plus £100 in interest. That’s how simple interest works.

Compound interest is more powerful. If, instead of lending someone just £100 the second year, you lend the whole £110 at the same interest rate, then they’ll pay you back £121 – that’s the £110 principal, plus £11 interest. The next year, you’ll get £133.10. If you keep reinvesting principal and interest, your money will grow exponentially. 

Let’s take a look at the numbers.

After re-lending 10 times, you’ll have earned nearly 160% on top of your principal. After 25 times, you’ll have earned nearly 900%! That’s the power of compound interest – the more times you reinvest your interest, the faster your investment grows.

How to calculate compound interest

An online compound interest calculator can calculate your interest for you (try the Motley Fool Savings Calculator!). But calculating compound interest yourself is fairly easy too. Better, it’ll help you to understand how the compound interest formula works.

The Compound Interest Formula

Above, each time we lent money, we worked out the interest and then added that to the principal. We can do that all in one go by multiplying the principal by (1 + interest rate). Let’s call the principal ‘P’ and the interest rate ‘r’. If we reinvest twice, we end up with:

P x (1 + r) x (1 + r)

We can write that more clearly as P(1 + r)²

To generalise that formula:

• P is the principal amount
• r is the interest rate
• n is the number of times we compound the interest in each time period
• t is the number of time periods.

That gives us the compound interest formula:

P (1 + r/n)^{n x t}

Let’s look at our original loan, when you lent £100 at a 10% annual interest rate. With annual compounding, if you lent it for 10 years, you’d end up with:

100 x (1 + 0.1/1)^(1×10) = 100 x 1.1¹⁰ = £259.73

What if they paid the same interest rate, but it compounded every month rather than every year? If you lent it for the same 10 years, you’d end up with:

100 x (1 + 0.1/12)^(12×10) = 100 x (1 + 0.1/12)¹²⁰ = £270.70

Understanding the compound interest formula helps you understand why you should check how often interest is compounded rather than just the interest rate. By compounding monthly rather than annually, you earned £11 extra.

The Rule of 72

There is a handy shortcut known as the Rule of 72 that you can use to estimate rates of return. It states that you can find out how many years it will take for your investment to double by dividing 72 by the percentage rate of growth.

So, it will take nine years for your investments to double if they grow at 8% a year (72/8=9). But it will only take six years if your investments grow at 12% and so on. The Rule of 72 only provides an approximate answer. But as shortcuts go, it’s sufficiently accurate for many calculations.

The benefit of compound interest

Compound interest grows your money in a savings account, term deposits, and bonds. However, the same principles – and the same compound interest formula – apply to any investment if you reinvest your profits. This is the key to building wealth over time.

What’s the downside of compounding interest?

There’s always a downside, and compound interest is no different. It’s brilliant if you’re the person earning interest, but not if you’re the one paying it. A credit card or loan can easily spiral out of control if you don’t keep up with repayments.

To avoid this, look for a 0% credit card to dodge the negative effects of compound interest.

The 5 Foolish Laws of Compounding

Here at the Fool, we like the concept of compound interest so much that we came up with the five Foolish Laws of Compounding.

1. Start early!

The earlier you start investing, the more time you leave for the miracle of compound interest to take effect. Someone who invests £100 a month from age 20 to 29 and then lets their investments grow, is likely to have more money at age 60 than someone who invests £100 a month from age 30 to 59.

2. Small differences in return matter. A lot!

Over long periods of time, the difference between investing at, say, 7% and 8% is enormous. If you don’t believe us, try experimenting with the financial calculators above.

3. Find a good balance for your life and money.

Investing isn’t everything. Like most things in life, it is best to strike a balance. With investing, it’s the balance between enjoying yourself now and providing for your future.

4. Over time, regular savings of small amounts can build up an astonishing sum of money.

If you save £100 a month for 40 years and your investments compound at 12% a year, how much will you have? The answer is an astonishing £980,000!

5. Time and patience are the friends of compounding and, therefore, of investing.

Saving for 40 years is obviously something you can’t do overnight. You have to exercise patience if you want to feel the full benefit of compounding.

Takeaway

The compound interest formula can help you understand what’s happening to your money, and why. If you keep reinvesting in a low-fee, high-interest account that compounds frequently, your wealth will grow. That’s the power of compound interest.