Financial Metrics · Basic level · 3 min read ·
What is compound interest?
Compound interest is the effect of calculating each period on the initial amount plus everything already generated before. What is generated also generates, so growth speeds up over time. Simple interest, by contrast, is always calculated on the initial amount only.
In 30 seconds
- With compound interest, each period is calculated on an ever larger amount.
- The gap with simple interest is small at first and large over the years.
- It works against you too: a debt with compound interest also grows faster and faster.
Why should you care?
Almost every rate you read, E.A., IRR or annual appreciation, already has compound interest built in.
- You understand why a monthly rate times twelve isn't the annual rate.
- You see why time weighs so much in any financial calculation.
- You recognize when a debt is growing faster than it seems.
Think of it as a rolling snowball
Each turn picks up more snow because the ball is already bigger. At first you barely notice; after many turns, the difference is huge. That is what compound interest does to an amount over time.
How does compound interest work?
- 1
Start from the initial amount
For example, 1,000,000 pesos.
- 2
Apply the period's rate
At 10% a year, year one generates 100,000 and the amount becomes 1,100,000.
- 3
Apply it again to the new amount
In year two the 10% is calculated on 1,100,000: it generates 110,000, not 100,000.
- 4
Repeat every period
Each year the base is larger, so what is generated grows too.
The formula
FV = PV × (1 + i)ⁿ
- FV
- = future value
- PV
- = initial amount
- i
- = rate per period, as a decimal
- n
- = number of periods
An example with numbers
As plain arithmetic, unrelated to any project: 1,000,000 pesos at 10% a year for three years.
| End of year 1 | 1,100,000 pesos |
|---|---|
| End of year 2 | 1,210,000 pesos |
| End of year 3 | 1,331,000 pesos |
| With simple interest, year 3 | 1,300,000 pesos |
| Difference from compounding | 31,000 pesos |
Over three years the gap is small. At the same rate over twenty years, the compounded amount reaches more than six times the initial one; the simple one, three times.
Where do you see it at Circular Urban?
There is no screen called compound interest, but it sits behind the estimated profitability in E.A. and the annual appreciation you see on the project sheet. Keep in mind that the distributions you receive don't add themselves back to your participation: compounding on them depends on what you do with that money. Every result is subject to the project's actual performance.
- Each project sheet, in the Profitability section, including Appreciation.
What changes in your finances once you get it
You use the rule of 72
Divide 72 by the annual rate to estimate how many years an amount takes to double: at 8%, about 9 years.
You start earlier
With compounding, time weighs more than the amount: saving earlier makes a big difference.
You watch your debts
Unpaid credit card interest compounds too, and the debt grows faster and faster.
Common mistakes
- Myth
10% a year for three years is 30% in total.
- In reality
With compound interest it is 33.1%: 1.1 × 1.1 × 1.1 = 1.331.
- Myth
Compound interest only applies to savings.
- In reality
It applies to any amount that grows by periods, including debts, which grow just as fast.
- Myth
If a project sheet shows an annual rate, my distributions compound on their own.
- In reality
Distributions are paid out to you; whether they keep generating depends on what you do with them.
Test yourself
You have 200 units at 10% a year with compound interest. How much do you have at the end of year two?
Keep learning
Helps to know first
This content is educational. Every participation carries risks inherent to the project, including the possibility of partial or total loss, and results are subject to each project's actual performance.
