What is compound interest?
Compound interest is interest calculated on both the original principal and previously accumulated interest. Because interest is earned on a growing balance, growth can accelerate over time.
Compound Interest Calculator
Use this compound interest calculator to estimate how invested principal can grow across years under recurring compounding assumptions.
Compound Interest Calculator
Convert equivalent annualized rates across different compounding frequencies to compare APR/APY-style quotes consistently.
Modify the values and click the Calculate button to use
Rate conversion
Results
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Input rate6%
Input basisMonthly (APR)
Output basisAnnually (APY)
Effective annual rate6.16778%
How the Compound Interest Calculator Works
Compound Interest Calculator
This calculator compound interest tool converts equivalent rates between compounding schedules so you can compare quoted rates on a like-for-like basis. If you need full balance growth projections with deposits and timelines, use the Interest Calculator for complete accumulation scenarios.
Users often search for terms such as Compound interest calculator SBI, Daily compound interest calculator, and Monthly compound interest calculator. The core math engine here supports those comparison workflows by normalizing rate assumptions across frequency choices.
What Is Compound Interest?
Interest is the cost of borrowing or the return earned for supplying capital. In practical finance, interest is usually expressed as a percentage of principal over time.
- Simple interest: calculated only on original principal
- Compound interest: calculated on principal plus previously earned interest
A key input in every example is the compound interest rate, because both return level and compounding interval affect final outcomes.
Compound interest is more common in modern lending and investing because balances are periodically updated and interest is applied to the new balance each cycle.
Simple vs Compound Interest (Quick Comparison)
Under simple interest, growth is linear because the interest base stays fixed. Under compound interest, growth accelerates over time because the interest base expands as earnings are added back into principal.
That difference may look small in early periods but can become substantial over longer horizons or higher rates.
Why Compounding Matters
Compounding can significantly amplify long-term portfolio growth when returns are positive and reinvested. The same mechanism can also increase borrowing cost when debt is carried for long periods.
This is why compound interest is often described as financially powerful in both directions: it rewards disciplined long-term investing and penalizes prolonged high-interest debt.
Different Compounding Frequencies
Rates can compound at different intervals such as daily, weekly, monthly, quarterly, semiannual, or annual. More frequent compounding generally increases effective annual yield for the same nominal rate.
For example, a nominal annual rate quoted with monthly compounding can map to a higher effective annual rate than the same nominal number compounded once per year.
APR, APY, and Frequency Conversion
APR-style quoting often references nominal annual rate, while APY-style quoting reflects compounding effect over a full year. Converting between frequencies helps prevent apples-to-oranges comparisons when reviewing loan or savings offers.
This calculator is specifically built for that conversion workflow.
Compound Interest Formulas
Basic Annual Compounding
A_t = A_0 * (1 + r)^t
- A_0 = starting principal
- A_t = value after t years
- r = annual rate (decimal)
- t = years
Compounding n Times Per Year
A_t = A_0 * (1 + r/n)^(n*t)
- n = compounding periods per year
- other symbols match the definitions above
This form is commonly used for monthly, weekly, and daily compounding assumptions.
Continuous Compounding
A_t = A_0 * e^(r*t)
Continuous compounding represents the mathematical limit of compounding frequency. In many practical cases, the difference versus daily compounding is small, but the formula is useful for theory, valuation models, and advanced finance study.
Rule of 72
The Rule of 72 is a quick estimate for doubling time under compound growth:
Years to double approx 72 / annual rate (%)
Example: at 8%, doubling time is roughly 9 years. It is a heuristic, not a precision formula, but useful for fast screening and intuition building.
Practical Use Cases
- Compare savings products with different compounding schedules
- Normalize lender quotes before choosing financing
- Estimate long-horizon growth sensitivity to frequency changes
- Build intuition for APY vs nominal-rate differences
- Build a quick compound interest table for planning checkpoints across multiple years
- Evaluate compound interest investments with conservative, baseline, and optimistic scenarios
- Assess whether a compound interest account matches your timeline and risk profile
Brief Historical Context
Compound interest ideas appear in very old commercial records and evolved through centuries of trade, banking, and mathematics. With modern finance, compounding became foundational to lending, savings, and investment valuation.
Later mathematical development around exponential growth and the constant e helped formalize continuous-compounding theory used in advanced economics and finance.
Key Takeaway
Compounding frequency, rate level, and time horizon jointly determine outcomes. Small differences in any one input can produce large differences over long periods.
Use this compound interest calculator for comparison and conversion; use detailed cash-flow models for final financial decisions.
Frequently Asked Questions
What is the compound interest on 6000 at 10% per annum for 2 years?
Using annual compounding: Amount = 6000 x (1 + 0.10)^2 = 7260. Compound interest = 7260 - 6000 = 1260.
How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily?
Using daily compounding, the result is approximately $1,127.49 after 2 years. This uses the formula A = P x (1 + r/365)^(365 x t) with P=1000, r=0.06, and t=2.
How much will $10,000 invested be worth in 20 years?
It depends on the return rate and compounding frequency. For example, at 8% annual compounding, $10,000 grows to about $46,610 after 20 years (10,000 x 1.08^20).
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal, while compound interest is calculated on principal plus previously earned interest. Over longer periods, compounding usually results in faster growth.
Why does compounding frequency matter?
Compounding frequency changes how often interest is added to the balance. More frequent compounding generally increases effective annual yield for the same nominal annual rate.
Is APR the same as APY?
Not exactly. APR is usually a nominal annual rate, while APY reflects the effect of compounding over a full year. This calculator helps convert between compounding bases for fair comparison.
What is continuous compounding?
Continuous compounding is the mathematical limit where compounding occurs infinitely often. It uses the formula with e^(rt) and is mainly used in advanced finance and theory.
What is the Rule of 72?
The Rule of 72 is a shortcut to estimate doubling time: divide 72 by the annual return percentage. For example, at 8%, doubling is roughly 9 years.
How accurate is this compound interest calculator?
It is accurate for interest-rate conversion across compounding frequencies. For full projections with variable cash flows, taxes, fees, or changing rates, use a more detailed scenario model.