Compound interest differs from simple interest because previously earned interest can become part of the base for later periods.
Interest can therefore be earned not only on the original principal but also on interest that has already been capitalized.
The longer the term and the more frequently compounding occurs, the more noticeable the difference from a simple-interest model can become.
The current LUKIK Compound Interest Calculator uses one initial principal and discrete compounding.
Compound-interest formula
Formula:
A = P × (1 + R / (100 × m))^(m × T)
Interest earned:
I = A − P
where:
P = initial principal;
R = nominal annual interest rate in percent;
m = compounding periods per year;
T = term in years;
A = future value;
I = interest earned.
Supported compounding frequencies
The calculator supports:
m = 1 — annually;
m = 2 — semiannually;
m = 4 — quarterly;
m = 12 — monthly.
For a term entered in months:
T = months / 12
Continuous compounding, arbitrary frequencies, contributions and withdrawals are not part of the current model.
Monthly-compounding example
Assume:
P = 100,000
R = 12%
T = 1 year
m = 12
The periodic rate used in the formula is:
12 / (100 × 12) = 0.01
Then:
A = 100,000 × (1 + 0.01)^12
Approximately:
A ≈ 112,682.50
Interest earned:
I ≈ 12,682.50
The resulting one-year growth is approximately:
12.68%
This is above the nominal 12% because compounding occurs repeatedly during the year.
How compounding frequency affects the result
For 100,000 at a nominal annual rate of 12% for one year:
| Compounding | Final amount | Interest | Growth |
|---|---|---|---|
| Annual | 112,000.00 | 12,000.00 | 12.00% |
| Semiannual | 112,360.00 | 12,360.00 | 12.36% |
| Quarterly | 112,550.88 | 12,550.88 | 12.55% |
| Monthly | 112,682.50 | 12,682.50 | 12.68% |
With the same nominal rate, more frequent compounding produces a slightly higher mathematical result.
How time changes compound growth
For 100,000 at 12% with monthly compounding:
| Term | Final amount | Interest earned |
|---|---|---|
| 1 year | ≈ 112,682.50 | ≈ 12,682.50 |
| 2 years | ≈ 126,973.46 | ≈ 26,973.46 |
| 3 years | ≈ 143,076.88 | ≈ 43,076.88 |
| 5 years | ≈ 181,669.67 | ≈ 81,669.67 |
The progression is not linear because the base changes after each compounding period.
Compound vs simple interest
Simple interest uses:
I = P × R / 100 × T
Previously earned interest does not increase the base.
Compound interest uses:
A = P × (1 + R / (100 × m))^(m × T)
and each later period works with a potentially larger balance.
That is why LUKIK keeps the deposit simple-interest calculator separate from compound-interest.
Using the LUKIK Compound Interest Calculator
Enter the initial amount, annual nominal rate, term and compounding frequency.
The calculator estimates future value, interest earned and growth for the selected scenario.
Calculate compound interest → LUKIK Compound Interest Calculator
Common mistakes
Using simple interest when compounding applies
Simple interest does not account for interest becoming part of the balance.
Confusing nominal rate and total growth
A 12% nominal rate with monthly compounding produces approximately 12.68% one-year growth in the example above.
Using an unsupported compounding frequency
The current calculator supports only 1, 2, 4 or 12 periods per year.
Adding contributions or withdrawals
The current model uses one initial lump-sum principal.
Assuming the mathematical result includes every real-world condition
Taxes, fees and other product-specific conditions are not included unless explicitly modeled.
Conclusion
Compound interest is calculated as:
A = P × (1 + R / (100 × m))^(m × T)
and:
I = A − P
Both time and compounding frequency affect the outcome.
The LUKIK calculator lets you compare annual, semiannual, quarterly and monthly compounding.
Open the LUKIK Compound Interest Calculator
FAQ
Which compounding frequencies are supported?
Annual, semiannual, quarterly and monthly.
Are regular contributions supported?
No. The current model uses one initial principal.
Is continuous compounding supported?
No.
Why can total growth exceed the nominal annual rate?
Because interest is compounded more than once during the year.