How Compound Interest Works: Formula, Compounding and Examples

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 th…

26/08/2026 0 comments
Share:
How Compound Interest Works: Formula, Compounding and Examples

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.