# The formidable power of compound interest

It was the great Albert Einstein who is credited with the legendary quote: “Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.” His adulation was echoed by English economist John Maynard Keynes, who marvelled at the sheer power of compound interest in his 1930 essay titled ‘Economic Possibilities for our Grandchildren’, and pondered the impossibility of it compounding forever.

Certainly, in the numerical sense, compound interest is infinite in both time and future value, which is why it is such an invaluable principle in the world of investment today. Compounding is the repeated addition of interest to the principal balance of a deposit. By reinvesting the interest, interest for subsequent periods is earned on the principal amount plus the previously accumulated interest, meaning the growth is exponential. This is in contrast to simple interest, which does not factor in interest earned over the previous period.

**Examples of compound interest calculations**

Imagine you were to invest £1,000 in a savings account which pays interest annually, with a return of 5 per cent. It’s easy enough to calculate how much you will have at the end of the first year – £1,050 (£1,000 + (£1,000 x 5%)).

However, at the end of your second year, you will have earned a total of £1,102.50 (£1,050 + (£1,050 x 5%). By compounding the interest i.e. adding it to the principal balance going forward, the annual interest received has increased from £50 to £52.50. By the third year, this increment rises to £55.13, taking the total value of the investment to £1,157.63 (£1,102.50 + (£1,102.50 x 5%).

Of course, the longer this goes on for, the greater the effect of the compound interest is, and after a certain number of years, the interest earned can exceed the amount of the principal. Here is the complete formula for calculating compound interest:

FV = P (1+r/n)^{nt }

[**FV** – Future Value; **P** – Principal; **r** – Rate; **n** – number of times compounded per year; **t** – number of years]

So, for the example above, if we plug in our respective numbers, we can determine that the principal of £1,000 would have doubled sometime during the 15^{th} year of the investment. There’s a handy ‘rule of thumb’ for working this out too, known as the Rule of 72. All you do is take the rate of interest you expect to earn, and divide it into 72. In our case, that would be 72/5, which is equal to 14.4. That is, during the 15^{th} year!

**Time and money**

What the above formulas and rules also demonstrate is that the earlier one starts investing, and the more frequently interest is received and compounded, the more they can take advantage of the most powerful factor of all – time. Take the example of two siblings – one who begins the above investment of £1,000 at the age of 20, and the other at 40. By the age of 60, the former will have accumulated £7,040, which is more than seven times the original investment – even without adding a penny to it along the way.

By comparison, the latter sibling, who made their investment 20 years later, will have accumulated just £2,653 by the time they reach the age of 60 (or 2.6 times the original investment). And here’s the kicker… the difference in value between their two investments will continue to diverge over time!

**Using compound interest to your advantage**

It would be remiss not to observe that compound interest also works both ways, and, in theory, applies to those who take out loans too. Indeed, if you were to borrow an amount of £1,000 at a rate of 5 per cent as per the above example, the amount owed would compound if you weren’t to make any loan repayments.

Generally, this isn’t much of a factor in practice, given that loans are usually repaid in monthly instalments i.e. the same frequency as the interest is applied. One exception, however, is student loans, whereby repayments are linked to earnings. This means that lower earners could end up paying an insufficient amount to keep pace with the compounding of the interest on their loan, and the amount owed simply keeps increasing – albeit that any outstanding debt is written off after 30 years.

Nevertheless, it shows the power of compound interest at both ends of the spectrum. Yet in the context of investment, it firmly demonstrates just how vital it is to start saving and investing as early as possible, and capitalise on the most important component of all in the equation – time. So even in these times of low interest rates, don’t be deterred… the time to start squirreling away money and building a portfolio is now!

**Related articles:**

- Cash ISA returns: The shame of high-street banks
- The ultimate guide to your first P2P investment
- Quick guide to how our interest rates work

Get email updates for future blogs: