How to use this interest calculator
Enter the initial principal, a nominal annual rate as a percentage, and a whole-year term from zero to one hundred. Select annual, quarterly, monthly, or daily compounding for the compound side. Both calculations use the same input rate; the simple side does not reinvest interest. The comparison assumes no later deposits or withdrawals. For regular deposits, use the Compound Interest Calculator. For durations stated in months or days, use the Simple Interest Calculator with its explicit time-unit and day-count settings.
How the calculation works
Simple interest grows in proportion to time because it applies the annual rate to the original principal. Compound interest grows geometrically because credited interest joins the balance on which later interest is calculated. These are different accumulation models, not interchangeable names for a quoted account rate. Comparing their results helps explain interest on interest while holding the starting principal and nominal rate constant.
With a nominal annual rate and n compounding periods per year, each compound period uses a rate of annual rate divided by n. Over t years there are n × t complete periods. This calculator uses whole model years so all supported frequencies have complete periods. Daily means 365 periods in every model year; it does not derive an actual calendar count, apply leap-day rules, or follow a provider's daily balance method.
A quoted effective annual yield already reflects a compounding convention. Entering that yield as a nominal annual rate and compounding it again can overstate the balance. For example, a nominal 5% rate compounded monthly has an effective annual rate above 5%. An account advertising 5% APY should not automatically be entered as a nominal 5% compounded monthly. Identify what the quoted rate means before using the comparison for any real product.
The difference is meaningful only within the stated assumptions. It does not include additional contributions, tax, fees, inflation, changing interest rates, market losses, withdrawal restrictions, or reinvestment delays. A fixed mathematical rate is not a prediction of investment performance. Likewise, an amortizing loan is a declining-balance problem and cannot be assessed by treating its original principal as a deposit growing untouched until the end of the term.
Formulas
Simple ending balance
Compound ending balance
Comparison
Worked examples
Annual compounding over two years
For 1,000 at a nominal 10% for two years, simple interest is 1,000 × 0.10 × 2 = 200, giving a 1,200 balance. Annual compounding gives 1,000 × 1.10² = 1,210. The extra 10 arises because the first year's 100 of interest also earns 10% during the second year.
Five years with monthly compounding
For 10,000 at a nominal 5% over five years, simple interest gives a 12,500 balance. Monthly compounding uses 60 periods at 0.05/12 and gives approximately 12,833.59. The difference is approximately 333.59 before fees or tax. This comparison assumes every credited interest amount remains in the account.
Zero rate and zero term
If the rate is zero, both models return the initial principal for any supported term. If the term is zero, neither model has had time to earn interest. A principal of zero with no later deposits likewise gives zero. These cases are useful checks before interpreting a larger scenario.
Common uses
Learn what reinvestment changes
Compare two accumulation rules using the same principal, nominal rate, and term. The extra compound amount arises from interest remaining in the balance, not a new deposit. This controlled comparison is useful when explaining why a constant annual percentage can produce different totals under different posting assumptions.
Check rate terminology
Use frequency changes to see the distinction between a nominal rate and an effective annual result. Before comparing actual savings products, identify whether each advertised percentage is nominal, effective, or an APY disclosure. A product comparison also needs fees, access rules, tax treatment, and any introductory-rate conditions.
Explore a time horizon
Increase the whole-year term while keeping other inputs unchanged to see linear simple accumulation and compound growth diverge. This is a mathematical sensitivity exercise. It should not be presented as a forecast of variable investment returns or as evidence that a longer commitment is always preferable.
Accuracy and limitations
Both balances use the same annual percentage converted to decimal form. The compound side divides its nominal rate by the selected frequency and uses complete periods; the simple side applies the annual rate once per year without capitalization. Rates and inputs must be nonnegative within the documented range.
The tool excludes later cash flows and assumes the principal remains available for the entire horizon. It cannot calculate an amortizing loan payoff, reproduce account-specific posting rules, or convert an effective yield automatically. Extremely large projections are rejected rather than shown as an unusable infinite result.
Sources and methodology
These references support the formulas and financial concepts explained on this page. Product-specific rates, fees, and contract conventions still need to be checked with the provider.
Frequently asked questions
Why compare the same annual rate?
Holding principal, nominal rate, and time constant isolates the effect of compounding. It does not by itself compare all costs or benefits of actual products.
Is the rate field APY?
No. The compound model uses a nominal annual rate divided by compounding frequency. APY already includes compounding and needs different treatment.
Can I add monthly savings?
Use the Compound Interest Calculator for regular deposits. This page keeps principal unchanged so the simple and compound comparison is directly interpretable.
Can compound growth ever equal simple growth?
Yes, for zero rate, zero time, or zero principal. With annual compounding over one year and no extra flows, the balances also match.
Does this model an installment loan?
No. Installment loans reduce principal as payments are made. Use the Loan Calculator to inspect the declining balance and scheduled interest.
Are the outputs guaranteed returns?
No. They are arithmetic illustrations under a constant rate. Actual account rules or investment outcomes can differ substantially.