Compounding has been famously called the eighth wonder of the world by Albert Einstein. It is the process where the interest you earn on an investment earns interest itself, causing your wealth to grow at an accelerating rate over time.
Unlike simple interest, which only pays returns on your original principal, compound interest reinvests your earnings, creating a snowball effect.
The Compound Interest Formula
To calculate compound interest, we use the following standard formula:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- $A$ = Maturity Amount (future value of your investment)
- $P$ = Principal investment amount (initial deposit)
- $r$ = Annual interest rate (expressed as a decimal, e.g., 6% = 0.06)
- $n$ = Number of times interest is compounded per year
- $t$ = Number of years the money is invested for
The Impact of Compounding Frequency ($n$)
The frequency of compounding determines how often interest is calculated and added to the principal balance. The more frequently interest is compounded, the higher your final balance will be:
- Daily Compounding ($n = 365$): Interest is calculated every single day.
- Monthly Compounding ($n = 12$): Interest is calculated 12 times a year.
- Quarterly Compounding ($n = 4$): Interest is calculated every 3 months.
- Yearly Compounding ($n = 1$): Interest is calculated once a year.
Compounding Frequency Comparison
Let’s see how an initial deposit of $10,000 grows over 10 years at a 6% annual interest rate under different frequencies:
- Simple Interest: Grows to $16,000 (Earns $600/year flat).
- Yearly Compounding ($n=1$): Grows to $17,908 (Earns $7,908 interest).
- Quarterly Compounding ($n=4$): Grows to $18,140 (Earns $8,140 interest).
- Monthly Compounding ($n=12$): Grows to $18,194 (Earns $8,194 interest).
- Daily Compounding ($n=365$): Grows to $18,220 (Earns $8,220 interest).
By moving from simple interest to daily compounding interest, you earn an additional $2,220 on the exact same principal and rate.
The Rule of 72
A quick mental math shortcut to find out when your investment will double is the Rule of 72.
Simply divide 72 by your annual interest rate:
$$\text{Years to Double} = \frac{72}{\text{Interest Rate}}$$
- At 6% interest, your money will double in approximately 12 years ($72 / 6$).
- At 8% interest, your money will double in 9 years ($72 / 8$).
- At 12% interest, your money will double in 6 years ($72 / 12$).