Compound interest is interest calculated not only on the initial principal, but also on the interest accumulated over time — a mechanism commonly known as interest on interest.
As interest is added to the principal, the total balance grows, and each new period generates additional interest based on this increasingly larger amount.
In practice, this creates an exponential growth effect. It is highly beneficial for long-term investors, but can be costly for individuals who take out long-term loans, since they end up paying interest on interest.
The standard formula used to calculate compound interest is:
A = P * (1 + r)^t
Where:
Suppose you make an initial investment of $10,000 at an annual interest rate of 10%. Let's calculate the amount after 3 years:
Let's substitute these values into the formula:
M = 10,000.00 * (1 + 0.10)^3
Calculating (1 + 0.10)^3:
(1 + 0.10)^3 = 1.10 * 1.10 * 1.10 = 1.33
Multiplying the principal by the result:
M = 10,000.00 * 1.33 = $ 13,310.00
Therefore, after 3 years, at an annual interest rate of 10%, an initial investment of $10,000 would grow to $13,310.
This means the investment increased by $3,310 due to the effect of compound interest.
Below is a complete breakdown showing how your investment grows over time:
| Month | Total Interest | Total Invested | Total Interest | Accumulated |
|---|---|---|---|---|
| 0 | -- | $ 10,000.00 | -- | $ 10,000.00 |
| 1 | $ 79.74 | $ 10,000.00 | $ 79.74 | $ 10,079.74 |
| 2 | $ 80.38 | $ 10,000.00 | $ 160.12 | $ 10,160.12 |
| 3 | $ 81.02 | $ 10,000.00 | $ 241.14 | $ 10,241.14 |
| 4 | $ 81.66 | $ 10,000.00 | $ 322.80 | $ 10,322.80 |
| 5 | $ 82.32 | $ 10,000.00 | $ 405.12 | $ 10,405.12 |
| 6 | $ 82.97 | $ 10,000.00 | $ 488.09 | $ 10,488.09 |
| 7 | $ 83.63 | $ 10,000.00 | $ 571.72 | $ 10,571.72 |
| 8 | $ 84.30 | $ 10,000.00 | $ 656.02 | $ 10,656.02 |
| 9 | $ 84.97 | $ 10,000.00 | $ 740.99 | $ 10,740.99 |
| 10 | $ 85.65 | $ 10,000.00 | $ 826.65 | $ 10,826.65 |
| 11 | $ 86.33 | $ 10,000.00 | $ 912.98 | $ 10,912.98 |
| 12 | $ 87.02 | $ 10,000.00 | $ 1,000.00 | $ 11,000.00 |
| 13 | $ 87.72 | $ 10,000.00 | $ 1,087.72 | $ 11,087.72 |
| 14 | $ 88.42 | $ 10,000.00 | $ 1,176.13 | $ 11,176.13 |
| 15 | $ 89.12 | $ 10,000.00 | $ 1,265.25 | $ 11,265.25 |
| 16 | $ 89.83 | $ 10,000.00 | $ 1,355.08 | $ 11,355.08 |
| 17 | $ 90.55 | $ 10,000.00 | $ 1,445.63 | $ 11,445.63 |
| 18 | $ 91.27 | $ 10,000.00 | $ 1,536.90 | $ 11,536.90 |
| 19 | $ 92.00 | $ 10,000.00 | $ 1,628.89 | $ 11,628.89 |
| 20 | $ 92.73 | $ 10,000.00 | $ 1,721.62 | $ 11,721.62 |
| 21 | $ 93.47 | $ 10,000.00 | $ 1,815.09 | $ 11,815.09 |
| 22 | $ 94.22 | $ 10,000.00 | $ 1,909.31 | $ 11,909.31 |
| 23 | $ 94.97 | $ 10,000.00 | $ 2,004.28 | $ 12,004.28 |
| 24 | $ 95.72 | $ 10,000.00 | $ 2,100.00 | $ 12,100.00 |
| 25 | $ 96.49 | $ 10,000.00 | $ 2,196.49 | $ 12,196.49 |
| 26 | $ 97.26 | $ 10,000.00 | $ 2,293.74 | $ 12,293.74 |
| 27 | $ 98.03 | $ 10,000.00 | $ 2,391.78 | $ 12,391.78 |
| 28 | $ 98.81 | $ 10,000.00 | $ 2,490.59 | $ 12,490.59 |
| 29 | $ 99.60 | $ 10,000.00 | $ 2,590.19 | $ 12,590.19 |
| 30 | $ 100.40 | $ 10,000.00 | $ 2,690.59 | $ 12,690.59 |
| 31 | $ 101.20 | $ 10,000.00 | $ 2,791.78 | $ 12,791.78 |
| 32 | $ 102.00 | $ 10,000.00 | $ 2,893.79 | $ 12,893.79 |
| 33 | $ 102.82 | $ 10,000.00 | $ 2,996.60 | $ 12,996.60 |
| 34 | $ 103.64 | $ 10,000.00 | $ 3,100.24 | $ 13,100.24 |
| 35 | $ 104.46 | $ 10,000.00 | $ 3,204.70 | $ 13,204.70 |
| 36 | $ 105.30 | $ 10,000.00 | $ 3,310.00 | $ 13,310.00 |
To calculate compound interest, you can use the formula mentioned earlier. Replace the known values in the formula and calculate the total amount (A).
Be sure to use the correct units for time and interest rate, ensuring both follow the same basis (for example, years and years, or months and months).
The main difference between simple interest and compound interest lies in how interest accumulates over time.
With simple interest, interest is calculated only on the initial principal. With compound interest, interest is calculated on both the principal and the previously accumulated interest.
In terms of results, compound interest tends to accumulate a larger amount over time than simple interest.
Compound interest offers several advantages for investors, and the most significant one is the potential for accelerated long-term capital growth.
As interest and dividends are reinvested, the total amount increases exponentially, allowing investors to expand their wealth more efficiently over time.
In other words, this represents higher long-term returns and can help investors achieve financial goals in less time.
To fully benefit from compound interest, investors can adopt the following strategies:
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