How to Use the Powerful Compound Interest Formula

Compound interest is something that financial advisers need to fully understand as it can have a serious effect on a client’s finances. It is also a topic that is regularly tested in various formats during the CII investment exams such as the R02 and AF4.

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.”

So what is compound interest?

It basically means that 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 maths for this is very simple:

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 years’ 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 twice-yearly 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

Remembering such a formula for an exam can be tricky, sometimes it’s easier to write the wording fully.

Future value = Present value(1 + interest rate)^{number of years}

This technique really comes in handy for some candidates when they need to learn a complex formula.

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

Future value = £10,000(1 + 0.05)⁵⁰  =£114,674

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.

1. Change the initial sum
2. Change the interest rate
3. Change the compounding period.

1. Initial sum:

• If you compound £100,000 at 5% over 50 years, you will have £1,146,740.
• If you compound £1,000,000 at 5% over 50 years, you will have £11,467,400.

Confirmation, if you still need it, that money makes money!

2. Interest rate:

• If your £10,000 sum compounds annually at 10% for 50 years, you will have the princely sum of £1,173,909.

• But only compound the same amount at 2% annually for 50 years, and you will have a rather disappointing £26,916.

This is the worrying outcome for anybody who invests in cash today’s climate. 

3. Compounding period:

• If you invest £10,000, but only compound at 5% for 10 years, you will have £16,289.
• If you invest £10,000, but only compound at 5% for 25 years, you will have £33,864.
• 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 shortcut 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 example, it takes 10 years for an investment to double in value, at a 7.2% compound return.

Summary

Compound interest is an essential lesson to understand. The three variables: interest rate, investment amount, and compounding period will all significantly impact your own or your client’s future wealth.

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

1. Write out the formula so you truly understand its meaning and application. Don’t just memorise it for the test.
2. Use colour to help visualise the content.
3. Practice the formula with as many different types of scenarios as possible.

Grab the resources you need!

If you’re studying for your CII R02 exam, and you’re wanting a feeling of confidence on exam day, grab our free taster to try out one of Brand Financial Training’s resources for yourself.  Click the link to download the R02 mock paper taster now!