Compound interest: how money grows on itself

Compound interest means you earn returns on your earlier returns, not just on what you put in. Time is the secret ingredient, which is why starting at 16 rather than 30 can make such a difference.

Simple versus compound

• Moneysmart explains that with compound interest you earn interest on your starting balance and on the interest you have already earned: 'This means you earn interest on your interest.'
• Simple interest is paid only on the original amount. AED 1,000 at 5 per cent simple interest earns AED 50 every year, so after 10 years you have AED 1,500.
• With yearly compounding at 5 per cent, year one adds AED 50, but year two adds 5 per cent of AED 1,050, which is AED 52.50, and so on.
• The formula for yearly compounding is: final amount = starting amount x (1 + rate) to the power of the number of years.

Worked example: AED 1,000 left alone

• AED 1,000 at 5 per cent a year, compounded yearly, grows to about AED 1,628.89 after 10 years, compared with AED 1,500 with simple interest.
• After 20 years it is about AED 2,653.30 (simple interest: AED 2,000).
• After 40 years it is about AED 7,039.99 (simple interest: AED 3,000).
• At 7 per cent a year the same AED 1,000 becomes about AED 1,967.15 after 10 years, AED 3,869.68 after 20 years and AED 14,974.46 after 40 years.
• Notice the growth speeds up: the second 20 years add far more than the first 20. These rates are illustrations only; real returns vary and can be negative in some years.

Worked example: starting early

• Imagine saving AED 100 a month into something that grows at an assumed 5 per cent a year, compounded monthly.
• Start at 16 and stop at 60 (44 years): you pay in AED 52,800 and end with about AED 191,613.
• Start at 30 and stop at 60 (30 years): you pay in AED 36,000 and end with about AED 83,226.
• The early starter pays in AED 16,800 more but ends with about AED 108,000 more, because the early money has longer to compound.
• Moneysmart's own advice is simple: 'The longer you save, the more your balance can grow. So start early.'
• Investments do not grow in a straight line. The FCA reminds long-term investors to be prepared to invest through short-term ups and downs in the market.

How often interest is added

• Interest can be added yearly, monthly or even daily. The more often it is added, the slightly faster the balance grows.
• Moneysmart's example: two people each put 10,000 dollars in at 5 per cent for 5 years. The one whose interest is added monthly ends with 12,834 dollars; the one paid at the end of the term ends with 12,500.
• The Bank of England explains that the savings rate tells you how much money will be paid into your account, so a higher rate means more money compounding for you.
• When comparing savings accounts, look at the annual rate that includes compounding, often called the annual equivalent rate or annual percentage yield.

The rule of 72 and its limits

• The rule of 72 is a quick mental shortcut: divide 72 by the yearly percentage rate to estimate how many years it takes money to double.
• At 6 per cent: 72 / 6 = 12 years. The exact answer is about 11.9 years, so the shortcut is very close.
• At 2 per cent: the rule says 36 years, the exact answer is about 35 years.
• The Corporate Finance Institute notes the rule is more accurate at lower rates and is meant for compound, not simple, interest. Our own calculation shows this: at 24 per cent it says 3 years, but the true figure is about 3.2 years; at 72 per cent it says 1 year, but the true figure is about 1.3 years.
• The same maths works against you with debt: a loan or card balance compounding at a high rate can double frighteningly fast.