Compound Interest Calculator

What Is Compound Interest?

Compound interest earns return on both the original principal and the accumulated interest from prior periods. This creates exponential rather than linear growth — small differences in time or rate compound into large differences in outcome.

Simple interest (for comparison) only earns return on the principal: $\text{Simple: } A = P(1 + rt)$

Compound interest earns on the growing balance: $\text{Compound: } A = P\left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ = Final balance
• $P$ = Principal (starting amount)
• $r$ = Annual interest rate (as a decimal, e.g., 5% → 0.05)
• $n$ = Compounding periods per year (1 = annually, 12 = monthly, 365 = daily)
• $t$ = Time in years

Practical Worked Example

Principal: 10,000 | Rate: 7% | Years: 10 | Compounding: Monthly

$r = 0.07$, $n = 12$, $t = 10$

$A = 10{,}000 \times \left(1 + \frac{0.07}{12}\right)^{120} = 10{,}000 \times 1.00583^{120} \approx 20{,}097$

At 30 years the interest earned is 7× the original principal.

Time dominates everything: The same 10,000 at 7% for 20 years yields 40,388. For 30 years: 81,165. Ten extra years nearly doubles the outcome — not because of any new deposits, but because interest begins earning interest on a larger base. Starting early usually matters more than small differences in compounding frequency or rate assumptions.

How Much Does Compounding Frequency Matter?

Less than most people expect. On a 10,000 deposit at 6% for 10 years:

Going from annual to daily adds only 313 over 10 years. Time and rate matter far more than frequency.

The Rule of 72

Divide 72 by the annual return to estimate years to double:

• 6% → doubles in ~12 years
• 9% → doubles in ~8 years
• 12% → doubles in ~6 years

This works because $\ln(2) \approx 0.693$ and 0.693 / 0.06 \approx 11.6$ years.

Real (Inflation-Adjusted) Return

The calculator shows nominal growth. To find real purchasing-power growth:

$\text{Real rate} \approx \text{Nominal rate} - \text{Inflation rate}$

A 7% nominal return with 3% inflation delivers approximately 4% real growth. That is the number that matters for retirement planning — not the nominal balance.

Common Mistakes to Avoid

Treating nominal return as real return. If your savings account earns 5% and inflation is 4%, your real purchasing power grows only 1%. Always subtract expected inflation when comparing long-term scenarios.

Expecting compounding frequency to dramatically change outcomes. The mathematical difference between monthly and daily compounding is less than 0.02% effective rate at typical savings rates. Choosing a product with lower fees or higher rate is worth far more.

Ignoring taxes on interest. In many jurisdictions, interest income is taxed annually — which prevents the full compound effect. Tax-advantaged or tax-deferred accounts can preserve more of the compound effect, but the rules depend on the country and account type.

Using a single optimistic rate for long-term projections. Investment returns fluctuate. A portfolio that returns 7% on average over 30 years might return −20% in some years. The actual balance at any point depends on the sequence of returns, not just the average.