Compound Interest – The Maths Behind Wealth Creation

Having an abundance of money alone, certainly isn’t going to bring great happiness on it’s own, but having financial freedom is surely a great positive. Imagine not having to worry about money, giving you the ability to focus on what you love instead of just taking a job to pay the bills. Unfortunately for many of us, this is the case until we save enough to live off, which is usually around the retirement age of 65. In this article we are going to show you that getting to that level is achievable.

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

Albert Einstein

What is compound Interest?

Compound Interest or Compounding Interest essentially means earning ‘interest on the interest’ as well as the initial value. In finance generally you can have simple interest where you earn x% a year on the initial deposit and the interest is taken out or you can have compound interest, where the interest made is reinvested each year. Therefore in the first year of saving with simple interest and compound interest the values are the same. However in the second year with compound interest you will earn more, because you have reinvested your profit.

As an example if you had £1,000 in an account with an interest rate of 10%, in the first year you would get: £1,000 x 10% = £100.

If you took advantage of compound interest and reinvested your profits in the 2nd year you would receive: (£1,000 + £100) x 10% = £110

This might seem like a small gain, hardly worth talking about, but the figures in the long term can be simply staggering. Just a small increase in the % interest or starting figures together with time can create huge increases.

Firstly we’ll look at the formula and then some examples of this.

The compound Interest Formula

If assuming that interest is annually the formula is very simple.

F = P x (1 + i)n

F = Final Amount
P = Principal or starting figure
i = Interest rate (i.e. 5% is 0.05)
n = number of years

Compound Interest Examples

% Interest Years Start Value End Value
2% 5 £1,000 £1,104
5% 5 £1,000 £1,276
10% 5 £1,000 £1,611
15% 5 £1,000 £2,011
2% 10 £1,000 £1,219
5% 10 £1,000 £1,629
10% 10 £1,000 £2,594
15% 10 £1,000 £4,046
2% 30 £1,000 £1,811
5% 30 £1,000 £4,322
10% 30 £1,000 £17,449
15% 30 £1,000 £66,212
2% 5 £25,000 £27,602
5% 5 £25,000 £31,907
10% 5 £25,000 £40,263
15% 5 £25,000 £50,284
2% 10 £25,000 £30,475
5% 10 £25,000 £40,722
10% 10 £25,000 £64,844
15% 10 £25,000 £101,139
2% 30 £25,000 £45,284
5% 30 £25,000 £108,049
10% 30 £25,000 £436,235
15% 30 £25,000 £1,655,294

 

In our examples we have chosen a realistic range of both initial investment values, interest rates and time scales.

In terms of the % interest rates, 2% is currently what people are getting in savings accounts if they are lucky. The higher rates can be achievable through the stock market (via value growth + dividends) and through property (via value growth + rental income). Hitting 15% is a difficult task, but some people do achieve this.

It’s also key to note that to achieve these figures, money cannot be withdrawn.

The key point is that just a small increase in any of growth rates, time or starting values can lead to a huge difference in the final balance.

 

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