Compound interest: the frenemy you need to know

The value of your investments and the income you receive from them can go up and down, and you may get back less than you invest. Any examples are for illustration purposes only.

When you use the gains from an investment to invest even more and hopefully produce even higher gains next time, you’re compounding. The theory is that by reinvesting your earnings, your portfolio has the potential to increase each year more than it would have if you spent your gains instead, which thankfully makes up for not having it in your hand.

If you keep reinvesting your profits over and over, your wealth should keep growing over time. On the flip side, when your credit card company charges you interest on top of the interest from the previous month, the amount you owe also compounds. This is the type of interest-on-interest growth you want to avoid at all costs.

Example

Imagine you invest £1,000 and achieve a 5% return annually (of course, the market isn’t that consistent and income is never guaranteed but it works for our example). Each year, you can either spend the earnings or reinvest them. At the end of 40 years, if you had chosen to spend the earnings each year, you would have an asset worth £1,000 plus 40 payments of £50 per year, or £3,000 in total. If you chose to reinvest the earnings, you wouldn’t have had any annual income but your initial investment will have compounded into an asset worth £7,040 - more than twice as much.

Remember though, when we talk about compounding for investment (non-bank) products, we have to take into account that actual returns will naturally vary and can be negative over periods of time. Any examples of compounding we use are for illustrative purposes only and don’t represent any actual financial product or investment return available.

Tell me more…

1. Why is compounding important for investors?
2. How do I calculate compound interest?
3. What does continuous compounding mean?

1. Why is compounding important for investors?

It’s not an explainer on compounding without the obligatory reference to Albert Einstein once calling compounding the eighth wonder of the world. Did he actually say it? Who knows, but we think he would have been a fan. What we do know is the capacity for growth from compounding can be pretty surprising. As we see in our example above, the longer you leave it to work its magic, the greater the effect.

Now, while exponential growth is a remarkable thing, you won’t be able to take a penny and turn it into £10m in three months. But, with the power of compound interest, it’s possible to help generate a tidy retirement pot. In fact, getting to grips with compounding by yourself, by reinvesting company dividends, or making sure your company is effectively doing the same thing with its own profits, is the basis of all good investing.

For example, a person saving £100 per month from the time of their 20th birthday until they retire at 65 (540 months) would mean they deposit £54,000 into their account. Now, assume they earn a hypothetical 5% interest on those savings each year. The total value of those 540 deposits on the person’s 65th birthday would be £196,930. In other words, the small monthly contributions turn into something much more meaningful thanks to compounding and time.

There are plenty of compound interest calculators out there but let’s walk through an example of annual compounding to explain how it works. Assume you hypothetically start with £100 in a cash account and let it grow at a 5% annual rate of return. The critical thing to remember is that you must not take that interest out in order for compounding to work.

At the beginning of the first year, you have £100. Then, at the end of the year, you earn 5% interest on that £100. So, at the end of year one, you have £105 – the initial investment plus the interest for the year using a ‘simple interest’ calculation.

Year 1 ending value = initial investment * (1 + interest rate)

Year 1 ending value = £100 * (1.5) = £105

At the end of the second year, you earn 5% interest again. But, that interest applies to the entire balance, not just the initial investment so the interest in year two is £5.25 (£105 x 5%). That is, you get another £5 in interest on the first £100 plus 25p from the £5 of reinvested earnings. The balance in your account is now:

Year 2 ending value = year 1 ending value * (1 + interest rate)

Year 2 ending value = £105 * (1.05) = £110.25

We can simplify this formula to:

Year 2 ending value = initial investment * (1 + interest rate)^2

This process works for any number of years. All you have to do is turn the exponent (that very last tiny number) into whatever year’s balance you’re trying to calculate. For example, if you want to know the balance after 10 years, the equation would be:

Year 10 ending value = initial investment * (1 + interest rate)^10

If you’re into a few more letters in your maths, you can also use the more general annual compounding formula of:

FV = PV * (1 + i)^n

Where:

• FV = future value
• PV = present value
• i = annual interest rate
• n = number of years

If you only want to know how much interest you’ve earned, you need to subtract the money you started with. That means the compound interest formula can be generalised to:

Compound interest = initial investment * (1 + interest rate)^n - initial investment

You might receive a yearly dividend from a company, that you want to reinvest. They might even pay these quarterly, or a fund you hold might pay monthly. As such, annual compounding is common but so are quarterly and monthly compounding. In some cases, compounding can be continuous. The closest mental image we can get to continuous compounding is to imagine calculating interest every second of every day.

Let’s step through the process. First, let’s say you want to calculate monthly compounding. You start with a hypothetical £100 and earn an annual interest rate of 10% on your account (that’s a high rate and not indicative of current interest rates but it works for our example). Because there are 12 months in a year, you need to divide the yearly interest rate by 12 to get the monthly interest rate. In this case, the monthly rate is 0.83%; (0.10 / 12).

Now we can solve for however many months we’re interested in. All you have to do is plug the number of months into the formula rather than the number of years:

Month n ending value = initial investment * (1 + monthly interest rate)^n

By compounding more frequently, you end up with a slightly larger number. You can see this by solving for the value at the end of year two, which is also the end of month 24.

Annual compounding: year two ending value = £110 * (1.1) = £121

Monthly compounding: month 24 ending value = £100 * (1.0083)^24 = £122.04

The continuous compounding formula looks like this:

FV = Pe^rt

Where:

• FV = future value
• P = principal
• e = is the mathematical constant for the base of the natural logarithm, which is approximately 2.7183
• r = interest rate
• t = time between the start and end value, expressed as the number of periods of the same length as the interest rate

For example, with continuous compounding after two years at an annual interest rate of 10%, we get:

Year two ending value = £100e^(0.1 * 2) = £122.14

Full to the brim of compounding goodness yet? Even if you can’t recite the alphabet soup of equations, just remember the power of compounding is generated through building growth upon previous growth and can really take off the longer you leave it. Just don’t let it work against you with things like bills and debts, otherwise that huge force will become your biggest enemy rather than your best friend.

Important information

When you invest your capital is at risk. The value of your investments, and the income you receive from them, can go down as well as up and you may get back less than you invest. Forecasts aren’t a reliable guide to future gains.

This article is meant for education purposes and should not be read as personal investment advice. Individual investors should make their own decisions or seek independent advice.