Compound interest
Increase your savings
Understanding how compound interest works can help you choose a
savings accounts or investment where your money works
harder for you. If your money is earning
compound interest, your savings will grow faster.
What is compound interest?
Compound interest is interest paid on the initial principal as well as the accumulated
interest on money you have borrowed or invested. Compound
interest is like double chocolate topping for your savings. You
earn interest on the money you deposit, and on the interest you
have already earned - so you earn interest on interest. An online
savings account paying monthly interest is an example of an account
that earns compound interest.
Compound interest is different from simple interest. With simple
interest, interest is paid at the end of a specified term, although
if the term is more than 12 months, interest may be paid annually.
A term deposit is an example of an account that earns simple
interest.
The compounding effect
If you invested $10,000 for 5 years at 5% per year, with
interest paid at the end of the term, you would earn $2,500 in
simple interest after 5 years, $500 for each year. This would give
you a total of $12,500 after 5 years.
If you invested $10,000 for 5 years at 5%, with interest
calculated and added monthly, you would earn $2,834 in
compound interest after 5 years, giving you a total of
$12,834. Returns would be higher because you'd earn
interest on the interest.
Here's how we calculated the figures in the example
above.
Simple interest on a $10,000 investment at 5% per year, paid at
the end of the term
| |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
| Deposit |
$10,000 |
$0 |
$0 |
$0 |
$0 |
| Interest |
$0 |
$0 |
$0 |
$0 |
$2,500 |
| Total |
$10,000 |
$10,000 |
$10,000 |
$10,000 |
$12,500 |
Compound interest on a $10,000 investment at 5% per
year, paid monthly
| |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
| Deposit |
$10,000 |
$0 |
$0 |
$0 |
$0 |
| Interest |
$512 |
$538 |
$565 |
$594 |
$625 |
| Total |
$10,512 |
$11,049 |
$11,615 |
$12,209 |
$12,834 |
Comparing compound and simple interest earnings on $10,000 at
5% per year
You can see how simple interest accrues at the
same rate each year while compound interest grows every
year. You will earn more money if you are paid compound
interest.
Work out how much interest you can earn on your savings.
Compound interest calculator
Compound interest
formula
If you're interested in doing your own compound interest
calculation, here's how.
Use the formula A = P x (1 + r)n
| Formula explanation |
| 'A' is the end amount of your investment |
| 'P' is the principal, i.e. the starting amount |
| 'r' is the percentage interest rate converted to a decimal rate
(e.g. 2% is 0.02) |
| 'n' is the number of time periods |
Example 1 - annual compounding
Work out what $2,000 will grow to over 2 years for an investment
or savings that grow at 5% per annum compounding
yearly.
A = $2,000 x (1.05)2
A = $2,000 x 1.1025
A = $2,205.00
Example 2 - monthly compounding
Work out what $2,000 will grow to over 2 years for an investment
or savings that grow at 5% per annum compounding
monthly.
First you need to divide the annual interest rate by 12, which
is 0.42%. You also need to calculate the number of time periods
('n') in months, which is 24.
A = $2,000 x (1.0042)24
A = $2,000 x 1.11
A = $2,211.64
Effective interest
rates
Not all financial institutions treat cash investments the same
way. Some compound interest monthly, others quarterly or even
annually. Some charge fees, others don't.
An effective interest rate, also known
as an effective yield or the annual percentage rate (APR), takes
all of this into account and expresses the rate in simple interest
terms.
Your balance at the end of a year is compared to your balance at
the beginning of the year and any increase is expressed as a
percentage of the opening balance. The effective interest rate is
the interest rate you would have been given, to achieve the same
closing balance, if you did not have the benefit of compounding
interest or been charged any fees.
Knowing the effective investment rate for an investment allows
you to compare it with accounts or investments offered by different
financial institutions.
The cost of delaying saving
If you're thinking of delaying your saving and making up for the
delay by saving a higher amount in the future, read the case study
below.
Case study: Nicky and Adam compare their savings
Nicky saves $50 per week for 10 years and puts her money into a
high interest savings account at 5% interest, compounding monthly.
The figures below show that she ends up with $33,644 after 10
years.
| |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |
Year 7 |
Year 8 |
Year 9 |
Year 10 |
Total |
| Deposits |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$2,600 |
$26,000 |
| Interest |
$60 |
$197 |
$340 |
$490 |
$648 |
$814 |
$989 |
$1,172 |
$1,366 |
$1,568 |
$7,644 |
| Yearly Total |
$2,660 |
$2,797 |
$2,940 |
$3,090 |
$3,248 |
$3,414 |
$3,589 |
$3,772 |
$3,966 |
$4,168 |
$33,644 |
Adam puts off his savings for 5 years but then saves double the
amount that Nicky does, $100 a week into a high interest savings
account for 5 years at 5% interest, compounded monthly. His balance
ends up being only $29,469.
| |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Year 6 |
Year 7 |
Year 8 |
Year 9 |
Year 10 |
Total |
| Deposits |
$0 |
$0 |
$0 |
$0 |
$0 |
$5,200 |
$5,200 |
$5,200 |
$5,200 |
$5,200 |
$26,000 |
| Interest |
$0 |
$0 |
$0 |
$0 |
$0 |
$121 |
$393 |
$679 |
$980 |
$1,296 |
$3,469 |
| Yearly Total |
$0 |
$0 |
$0 |
$0 |
$0 |
$5,321 |
$5,593 |
$5,879 |
$6,180 |
$6,496 |
$29,469 |
Nicky started her saving earlier so she got the benefit of
compound interest for the first 5 years. This made a big difference
to her final balance. In many cases, even if you double your
deposits at a later date, you may never catch up to people who
start saving earlier.
Understanding how compounding works will help
you to make better decisions on when to start saving and which
account to choose.
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Last updated: 20 Jun 2017
