Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Compound interest can be thought of as "interest on interest," and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

While compound interest is usually used to refer to interest earned on loans or deposits, the principles can be applied equally to investing.

This article explains compound interest from the investing perspective.

How compound interest works for investing

Compound interest in the investing context is the return you earn on:

• your initial investment (often called the principal)

• the returns you've already earned (capital growth and dividends to-date)

For example, if you have investments held with Pearler, you'll earn returns on your initial investment and on the capital growth of that investment to-date in any given year. You'll also earn returns on your dividends if you've chosen to re-invest them.

You get interest on your interest, or in this case a return on your return.

Invest more with compound interest

The power of compounding helps you to invest more money. The longer you invest, the greater your returns over the long-term. So start as soon as you can and invest regularly. You'll earn a lot more than if you try to catch up later.

For example, if you invested $10,000 into an ETF that spread your money across the entire Australian sharemarket (a.k.a. All Ordinaries) and the returns were consistent with the average total annual return over the last forty years (which they may not be), then you would expect a 10% annual return:

• After five years, you'd have $16,105. You'd earn $6,105 in "interest".

• After 10 years you'd have $25,937. You'd earn $15,937 in "interest".

• After 20 years you'd have $67,275. You'd earn $57,275 in "interest".

Use the investing compound interest calculator [to-do: link]

Work out how much you can earn in interest if you start investing now.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r) ^ n

A = ending balance
P = initial investment (or principal)
r = interest / total return rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods

How to calculate compound interest

To calculate how much $1,000 will earn over twenty years at a total return rate of 10% per year, use the compound interest formula:

A = P x (1 + r) ^ n

A = $1,000 x (1 + 0.1) ^ 20
A = $6,727.50

Use dividend reinvestment plans to maximise compound interest

Compound interest is all about earning interest on interest thus, the way to maximise compound interest is to:

1. Reduce the amount of time between receiving and re-investing any interest

2. Minimise the cost incurred when re-investing interest

For sharemarket investments, dividend reinvestment plans provide both the fastest and cheapest way to reinvest dividends (and sometimes you also get a discount, depending on the share you've invested in).

Interested in learning how to set up your dividend reinvestment plan? [insert link]

Variable compound interest (shares) vs fixed compound interest (cash)

As covered earlier, compound interest is typically applied to cash investments such as loans and deposits which have an agreed and reliable rate.

In the sharemarket investing context, returns or "interest" is not reliable as it is for cash investments, and therefore to apply compound interest principles you need to make projections about what the future return will be.

Generally, making projections about returns based on past performance is a bad idea. However, if your investment is sufficiently diversified and will be held for a sufficiently long time period, then it is fair to use past performance as a guide if returns are averaged over a sufficiently long time period.

An example of this would be incrementally investing in an all-world ETF, holding it for 20 years, and assuming that the average annual return each year will be the average of the past 20 years (~8%).

The reason investors choose the variable return of sharemarket investments over the fixed return of cash investments is that returns of shares are higher, on average. If investors have sufficiently long investing horizons and high risk tolerances, then sharemarket investments are the better investment option.

On the flipside, the reason investors choose the fixed return of cash investments over shares is reliability - investors can usually expect a reliable, steady return from cash investments. If investors have short-term cash needs and/or low risk tolerances then cash investments are the better option.

Case Study

Michael and Sophie compare variable vs fixed compounding

Michael and Sophie both decide to invest $10,000 for 10 years. Michael chooses to invest in a 10-year term deposit which offers a 3% interest rate, with interest paid annually. Sophie chooses to invest in an all-world ETF and re-invest all her dividends.

During the first year the world's sharemarket dropped by 10%, at the end:

• Michael's investment is worth $10,300 (10,000 x 1.03)

• Sophie's investment is worth $9,000 (10,000 x 0.9)

After the first year, the world's sharemarket rallied and experienced an average increase of 12% per annum until the end of the fifth year:

• Michael's investment is worth $11,593 (10,000 x 1.03 ^ 5)

• Sophie's investment is worth $14,162 (10,000 x 0.9 x 1.12 ^ 4)

From the fifth to tenth years, the sharemarket experienced stable growth and averaged an 8.8% per annum return:

• Michael's investment is worth $13,439 (10,000 x 1.03 ^ 10)

• Sophie's investment is worth $21,589 (10,000 x 0.9 x 1.12 ^ 4 x 1.06 ^ 5)

Sophie and Michael both started with the same amount. But Sophie gets $8,150 more than Michael because she opted for the more volatile investment vehicle which has a higher expected return.