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The math behind the millions: understanding the power of compound interest over time

Compound interest is the mechanism that allows investors to make the most of their money and reap rewards.

Published Feb 13, 2024

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By: Nirdev Desai

It was Albert Einstein who called compound interest the “eighth wonder of the world”, saying that “he who understands it, earns it. He who doesn’t pays it”.

In the investment world, compound interest is the mechanism that allows investors to make the most of their money and reap the rewards of patience, perseverance, and consistency.

Understanding and leveraging the power of compound interest can be a game-changer.

Simple vs compound interest

One of the best ways to understand how compound interest works is to start by understanding what it is not. Simple (or fixed) interest is a straightforward concept in finance that involves the accumulation of interest on a principal amount over a defined period. Unlike compound interest, simple interest is calculated only on the original principal amount and not on the growth of the principal amount over time.

This can be illustrated by way of an example. In scenario A, a client invests R100 000 in an account that pays simple interest of 10% on their capital for a period of three years.

At the end of the investment period, the simple interest earned on the investment will be calculated as follows: R100 000 X 10% X 3 (years), which amounts to R30 000. The total value of the investment would then be R130 000.

If the same client were to invest the same amount of capital in an account that pays compound interest, the value of the investment would be greater than in the case of scenario A.

After the first year, the interest earned would amount to R10 000 (R100 000 X 10%). In the second year, the client would earn 10% interest, but not on the same, original principal amount.

Instead, compound interest would be calculated on the original capital value plus the interest earned in year 1, i.e. R110 000 as at the end of the first year.

In the second year therefore, interest earned would amount to R11 000 (R110 000 X 10%), bringing the investment’s total value at the end of year two, to R121 000.

Likewise, in the third year, the compound interest would amount to R12 100 (R121 000 X 10%), bringing the total value of the investment to R133 100.

Comparing scenario A, in which the investment earned simple interest, and scenario B, in which the client earned compound interest, will reveal that simply by opting for compound interest, the client earned R3 100 more, or just over 10% more in cumulative returns – this compounds even further with time.

As this example illustrates, the underlying concept of compound interest is that you earn interest on an ever-increasing base, instead of only on the original amount. While the differences may seem small in the short run, they can add up powerfully in the long run.

All in good time

Compound interest has immense power to make money grow, but the factor that harnesses its true power is time.

The more an investment is left to grow and earn compound interest, the greater the earning potential becomes. This can have major implications on investments that are made towards saving for retirement or other long-term goals.

Retirement annuities and tax-free savings account offer some of the easiest ways to benefit from compound interest.

These investments are also both exceptionally tax-efficient – if investors can commit themselves to having the discipline to make regular contributions, compound interest will do the rest.

To understand how compound interest can work for you over time, consider a scenario in which two investors start saving in an RA.

For anecdotal purposes, the compound interest return could be set at 10% per annum with a 6% increase per annum on each investor’s contributions to counteract the effects of rising inflation.

Investor one starts saving for retirement at the age of 20 with a monthly contribution of R500 (the investment term to retirement at age 65 is 45 years). Investor two only starts saving at the age of 35 (investment term 30 years).

At the end of the investment period, the accumulated value of the RA will be the same in both scenarios, but investor two will have had to contribute R2 500 per month to end up with the same amount as investor one at retirement.

In other words, investor two would have had to invest 3.33 times as much as investor one, to achieve the same results.

This example demonstrates the importance of starting as early as possible when it comes to saving for retirement, but also the fact that time is the secret ingredient to making the most of the power of compound interest.

Advisers are in the best position to help their clients tap into this power and structure their portfolios in a way that aligns with their goals and maximises their returns.

As there are many complexities to a financial plan, it’s important to work alongside a qualified financial adviser who will help guide you through the important factors that will eventually affect your retirement savings goal.

* Desai is the head of sales at PSG Wealth.

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