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# How to use the POWERFUL compound interest formula

It will also come up in various formats during any investment examination you take.

As Albert Einstein is famous for saying (even if he may not have actually said it):

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

Or this quote from investor Charlie Munger,

“Understanding both the power of compound interest and the difficulty of getting it is the heart and soul of understanding a lot of things”

**So what is compound interest?**

It basically means the interest you receive is not only paid on your initial investment, but also on the previous interest received.

It is the foundation of any long-term, successful and sustainable investment strategy.

So as an example:

In year one, £100 at 5% interest equals £105.

In year two, £105 at 5% interest equals £110.25

This appears a very small difference, but when you factor in ** time** the effect of compound interest is huge.

**Simple interest**

£10,000 invested for 50 years at 5% simple interest (or not compounded) becomes £35,000.

The math for this is rather simple (excuse the poor pun):

5% of £10,000 = £500

£500 x 50 years = £25,000 (this is the interest earned)

Add the interest earned, £25,000, to the original sum, £10,000, provides £35,000 in 50 years time.

**Compound interest**

With compound interest however, the sum in 50 year’s time becomes £114,674.

That’s a huge difference.

This is only compounding annually, you can slightly increase this if you compound more frequently, such as the semi-annual coupon repayments on a bond. I won’t go into this just yet.

Here’s the formula for this:

**FV=PV(1+r) ^{n}**

**Where:**

**FV = Future value**

**PV = Present value**

**r = Interest rate**

**n = Number of years**

Whilst I can remember such a formula for an exam, I find it difficult to fully understand the math and it’s meaning without writing down the wording fully. I also like to use colour.

So here’s how I understand the formula.

Whilst you can simply input the numbers into a calculator and it will display the answer, I also find it helpful to write down the figures and follow the calculation steps.

**The effect of the different variables**

You should use the formula in as many practice examples as possible and try to change all the variables, so you can fully understand the effects of compound interest.

- Change the initial sum
- Change the interest rate
- Change the compounding period.

**Initial sum**

If you compound £100,000 at 5% over 50 years, you will have £1,146,739.

If you compound £1,000,000 at 5% over 50 years, you will have £11,467,399.

*Confirmation, if you still need one, that money makes money!*

**Interest rate**

If your £10,000 sum compounds annually at 10% for 50 years, you will have the princely sum of £1,173,908.

But only compound at 2% annually, and you will have a rather disappointing £26,915.

*This is the worrying outcome for anybody who invests in bonds in today’s climate. With 30-year gilts yielding just 2.27%, their future wealth is going to be severely impacted.*

**Compounding period**

If you invest £10,000, but only compound at 5% for 10 years, you will have £16,288.

If you invest £10,000, but only compound at 5% for 25 years, you will have £33,863.

But if you wait the full 50 years, you will have £114,674.

*This shows how important patience is, how important it is to save early, and how much early retirement can affect your overall wealth.*

**The rule of 72**

A final way to help understand compound interest is the rule of 72.

The rule provides a quick short cut to calculate how long it will take to double your investment at a set interest rate.

**Years required to double investment = 72 / compound interest rate**

So for examples, it takes 10 years for an investment to double in value, at a 7.2% compound return.

Going back to the 30-year gilt rate of 2.27% I mentioned earlier, it will take roughly 32 years for your money to double in value. Not exactly an appealing prospect!

**Summary**

Compound interest is an essential lesson to understand. The three variables will all significantly impact on your own or your client’s future wealth.

When learning this or any other formula, try and remember these things:

- Write out the formula so you truly understand its meaning and application. Don’t just remember it for a test.
- Use colour to help visualize the content.
- Practice the formula with as many different types of scenarios as possible.

I hope this helps.

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