Compound Interest Calculator
Grow a principal with A = P(1 + r/n)^(nt), or continuously with A = Pe^(rt). Compare the compound interest earned with simple I = Prt, and solve for the time that reaches a target amount.
Interest $157.63 · simple would be $150.00
- Write the annual rate as a decimal: 5% = 0.05.
- A = 1000 × 1.05³ = $1,157.63.
- Compound interest is $157.63; simple interest would be $150.00.
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How to Use the Compound Interest Calculator
Find Amount grows a known principal. Find Time solves for t from a target amount using a logarithm. Choose how often interest is credited, including the continuous limit.
- Pick Find amount A or Find time t.
- Enter dollars and an annual percent. Time is in years (18 months is 1.5).
- Choose n, then Calculate. Read A or t, the interest earned, the effective annual rate, and the simple-interest comparison.
I = Prt with no compounding belongs on the Simple Interest Calculator. A monthly loan payment belongs on the Loan Calculator. The logarithm used to solve for t is shown step-by-step on the Logarithm Calculator.
The Compound Interest Formulas
Each compounding period multiplies the current balance by (1 + r/n). After nt periods the product is (1 + r/n)^(nt). As n grows, that factor approaches e^(rt). The effective annual rate is (1 + r/n)^n − 1 (or e^r − 1 when compounding is continuous). It is the one-year growth you actually get from a quoted nominal rate r.
Compound Interest Examples
$1,000 at 5% for 3 years, annually
A = 1000 × 1.05³ = $1,157.625, which displays as $1,157.63. Interest is $157.63. Simple interest is $150.
The same data, monthly
A = 1000 × (1 + 0.05/12)^36 ≈ $1,161.47. More frequent compounding earns a little more.
Continuous compounding
A = 1000 × e^(0.15) ≈ $1,161.83. That is the n → ∞ limit of the monthly figure.
A 0% rate
A stays $2,000 after 2 years. No interest is added, compound or simple.
Time to double $1,000 at 5% annual
t = ln(2) / ln(1.05) ≈ 14.207 years. The “rule of 72” guess 72/5 = 14.4 years is close.
Target smaller than the principal
Growing $2,000 at a positive rate cannot produce $1,000 in positive time. The calculator rejects that pair.
Compound vs Simple Interest
Simple interest charges r only on the original P for the whole time t. Compound interest charges r on the current balance, so interest itself earns interest. The two match for one year with annual compounding; they drift apart as t or n grows. A fixed monthly loan payment is a third model — amortization — on the Loan and Mortgage pages.
Common Compound Interest Mistakes
Leaving 5% as 5 in the formula
r is 0.05. Using 5 produces a factor of 6 per year.
Using n = 12 but leaving t in months
t is years. Three years of monthly compounding is n = 12 and t = 3, so nt = 36 periods. Do not also convert t to 36.
Treating APY as the nominal rate
The quoted r is nominal. The effective annual rate is larger when n > 1.
Using this page as a loan payment
A = P(1+i)^n grows a deposit. A monthly payment that retires a balance is a different formula on the Loan Calculator.
Solving for t without a log
You cannot isolate t from A = P(1+r)^t by dividing. Take ln of both sides, or use Find time here.
Compound Interest Calculator FAQs
What is the compound interest formula?
A = P(1 + r/n)^(nt) for n compounding periods per year. Continuously, A = Pe^(rt). Interest earned is A − P.
How is this different from simple interest?
Simple interest is I = Prt on the original principal only. Compound interest applies r to the growing balance.
What is the effective annual rate?
(1 + r/n)^n − 1, or e^r − 1 if compounding is continuous. It is the actual one-year percent growth.
How do you solve for time?
t = ln(A/P) / (n ln(1 + r/n)). That is a logarithm. The Logarithm Calculator shows the same change-of-base step.
Is this investment or lending advice?
No. It is an educational evaluation of the classroom formulas. Real accounts add fees, taxes, and changing rates.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is for general educational use. It is not investment, tax, or lending advice. Review important results before relying on them.