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What is the compound interest formula?

By:  Nic Gardner | 1st August 2021

If you’ve heard anything about saving and investing, you’ll have heard about “the power of compound interest!” But what is compound interest? How does it work? Why is it important? And what’s the compound interest formula? Let’s take a look.

What is compound interest?

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.

If you lend your money, the borrower will pay you back, with a fee on top. This fee is interest, and it’s usually a percentage of the money you lent them.

If you lend me £100 at 10% interest, then I’ll pay you back £110 – that’s the original £100, which we call the principal, plus £10 interest. You could keep lending me the same £100, and earning £10 each time. After ten 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 me just £100 the second time, you lend me the whole £110 at the same interest rate, then I’ll pay you back £121 – that’s the £110 principal, plus £11 interest. The next time, 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.

  Principal (amount lent) 10% interest Total repaid Total profit
1 £100.00 £10.00 £110.00 10%
2 £110.00 £11.00 £121.00 21%
3 £121.00 £12.10 £133.10 33.1%
4 £133.10 £13.31 £146.41 46.41%
5 £146.41 £14.64 £161.05 61.05%
6 £161.05 £16.10 £177.16 77.16%
7 £177.16 £17.72 £194.87 94.87%
8 £194.87 £19.49 £214.36 114.36%
9 £214.36 £21.44 £235.79 135.79%
10 £235.79 £23.58 £259.37 159.37%

 

After re-lending ten times, you’ll have earned nearly 160% on top of your principal. After twenty-five 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 can you calculate compound interest?

You can calculate it one step at a time or use an online calculator (try the Motley Fool Savings Calculator!), but it’s easy to calculate yourself. Better, it’ll help you understand how the compound interest formula works.

Above, each time we lent money we worked out the interest, 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:

That gives us the compound interest formula:

P (1 + r/n)n x t

Let’s look at our original loan, when you lent me £100 at 10% interest. If it compounded annually, and you lent it to me for 10 years. You’d end up with:

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

What if I paid the same interest rate, but it compounded every month rather than every year? If you lent it to me 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

So you see, 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.

How can you benefit from compound interest?

In reality, my friends don’t pay me interest when I lend them money – but my bank does! Compound interest grows your money in savings accounts, term deposits, and bonds. However, the same principles – and the same compound interest formula – apply to any investment if you reinvest your profits.

What’s the downside?

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. Credit cards and loans can easily spiral out of control if you don’t keep up with repayments.

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

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.

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