How to Use This Calculator
This page combines four common interest scenarios in a single tool. Pick the tab that matches your situation, enter the principal (or monthly contribution), an annual interest rate, and a term. Results update as you type.
- Savings (Lump Sum) ??for a one-time deposit such as a savings account, certificate of deposit (CD), or fixed-term deposit. Choose simple, monthly compounding, or yearly compounding.
- Recurring Deposits ??for accounts where you contribute the same amount each month. Simple mode treats each contribution as earning interest until maturity; compound mode adds interest to the balance every month.
- Loan ??produces a month-by-month payment schedule. Amortizing keeps the total payment constant; Equal Principal pays the same principal each month plus a shrinking interest amount; Interest-Only / Bullet pays interest each month and the full principal at the end.
- Simple vs Compound ??uses the same inputs to show how compounding frequency changes the final balance.
The optional tax field reduces gross interest by the rate you enter. In the U.S., interest from savings and CDs is generally taxed as ordinary income at the federal level, and many states tax it as well.[1]
Simple Interest
Simple interest is calculated only on the original principal, not on accumulated interest. It is the easiest way to model short-term loans and certain savings products that do not reinvest earnings.[2]
Example: $10,000 deposited at 5% simple interest for 3 years earns $10,000 횞 0.05 횞 3 = $1,500 in interest, regardless of how often interest is credited.
Compound Interest
Compound interest is earned on the principal plus any interest already credited. The more often interest is added to the balance, the faster the balance grows.[3]
Example: $10,000 at 5% compounded monthly for 3 years grows to $10,000 횞 (1 + 0.05/12)^36 ??$11,614 ??about $114 more than simple interest over the same horizon. Over 30 years, the gap widens dramatically: simple interest yields $25,000 of interest, while monthly compounding yields more than $34,800.
Compounding Frequency
The same nominal rate produces different ending balances depending on how often interest compounds. The continuous-compounding limit, A = P 횞 e^(rt), sets the theoretical ceiling.
- Annually ??interest added once per year. Common for fixed-rate bonds.
- Semi-annually ??twice a year. Typical for U.S. Treasury bonds.
- Quarterly ??four times a year. Some money-market accounts.
- Monthly ??twelve times a year. Most savings accounts, CDs, and mortgages.
- Daily ??used by many checking and high-yield savings accounts; the practical difference versus monthly is usually small.
The Annual Percentage Yield (APY) translates any compounding frequency into a comparable annual figure: APY = (1 + r/n)^n ??1.[4]
The Rule of 72
A quick mental shortcut for compound interest: divide 72 by the annual rate (in percent) to estimate how many years it takes for an investment to double.[5] At 6%, money doubles in roughly 72 첨 6 = 12 years. The approximation is accurate within about one year for rates between 6% and 10%, and less accurate at very high or very low rates. For more precision, use the natural-log form: years to double = ln(2) 첨 ln(1 + r) ??0.693 첨 r.
Fixed vs. Variable Interest Rates
A fixed rate stays the same for the entire term, so you can model the outcome with certainty. CDs, most mortgages, and many personal loans use fixed rates.
A variable (or floating, adjustable) rate changes as a benchmark moves. In the United States, common benchmarks include the federal funds rate set by the Federal Reserve and the Secured Overnight Financing Rate (SOFR), which replaced LIBOR for most new contracts.[6] Adjustable-rate mortgages (ARMs), credit cards, and home-equity lines of credit (HELOCs) usually carry variable rates. This calculator assumes the rate you enter holds for the full term ??if you expect the rate to change, run the calculation again with the new value.
Periodic Contributions
Adding money on a regular schedule ??payroll deductions into a savings account, monthly transfers into a brokerage, or automated CD additions ??accelerates growth because each contribution starts earning interest from the date it lands. The Recurring Deposits tab models a fixed monthly contribution. Two timing conventions exist: ordinary annuity (deposit at the end of each period) and annuity due (deposit at the beginning). This calculator uses the deposit-at-start convention so that every contribution earns at least one full month of interest in compound mode.
Loan Repayment Methods
Amortizing (Equal Total Payment)
Every monthly payment is the same. Early payments are mostly interest; later payments are mostly principal. This is the standard for U.S. fixed-rate mortgages and most personal loans. The monthly payment is given by:
Equal Principal
The principal portion is the same every month, but interest shrinks as the balance falls, so each payment is smaller than the last. The first payment is the largest. This structure is less common in U.S. consumer lending but appears in some commercial loans.
Interest-Only / Bullet
Only interest is paid each month; the entire principal is repaid in a single balloon payment at maturity. Used in some construction loans, bridge loans, and corporate bonds.
Tax on Interest Income
In the United States, interest from savings accounts, money-market accounts, CDs, and most bonds is taxed as ordinary income at the federal level. The financial institution generally issues Form 1099-INT for amounts of $10 or more.[1] Most states also tax interest income, though a handful do not levy a state income tax. Municipal-bond interest is usually exempt from federal income tax, and interest on U.S. Treasury securities is exempt from state and local income tax ??neither of which is fully captured by a single combined-rate input.
Enter your combined marginal rate (federal + state, plus any local tax) in the Tax field to see the after-tax outcome. Leave it blank to see the gross result. Tax-advantaged accounts such as a Roth IRA or a 529 plan have their own rules and are not modeled here.
Inflation and Real Return
The rate displayed on a deposit or loan is the nominal rate. The real rate adjusts for inflation and is what determines purchasing power over time. The Fisher equation links the two:[7]
U.S. inflation, as measured by the Consumer Price Index, has averaged roughly 3% per year over the long run but has varied widely from year to year.[8] If your savings earn 4% in a year when inflation is 3%, your real return is about 1%. If inflation outpaces your interest rate, your money loses purchasing power even though the nominal balance grows. This calculator reports nominal results; to estimate the real outcome, subtract the inflation rate from the interest rate before entering it.
Frequently Asked Questions
Are the results guaranteed to match what my bank pays?
No. Banks may use slightly different day-count conventions (actual/365 vs. 30/360), round at different stages, or apply tiered rates above certain balances. Treat this calculator as a planning tool, not a contract.
Does it model early withdrawal penalties on CDs?
No. CD early-withdrawal penalties vary by bank and term. If a penalty applies, subtract it manually from the after-tax result.
What about variable-rate scenarios?
The calculator assumes the rate is constant for the full term. To explore a rate change, run the calculation twice ??once for the period before the change and once for the period after ??using the ending balance of the first run as the starting principal for the second.
Why does my loan show a slightly different last payment?
The amortizing formula produces a payment with fractions of a cent. The final payment in real loans is usually adjusted by a few cents so the balance lands exactly on zero. This calculator does not perform that final rounding.
References
- [1] U.S. Internal Revenue Service, Topic No. 403 ??Interest Received. irs.gov/taxtopics/tc403
- [2] Wikipedia, "Interest" (CC BY-SA 4.0). en.wikipedia.org/wiki/Interest
- [3] Wikipedia, "Compound interest" (CC BY-SA 4.0). en.wikipedia.org/wiki/Compound_interest
- [4] U.S. Consumer Financial Protection Bureau ??APY. consumerfinance.gov
- [5] Wikipedia, "Rule of 72" (CC BY-SA 4.0). en.wikipedia.org/wiki/Rule_of_72
- [6] Federal Reserve Bank of New York ??SOFR. newyorkfed.org/markets/reference-rates/sofr
- [7] Wikipedia, "Fisher equation" (CC BY-SA 4.0). en.wikipedia.org/wiki/Fisher_equation
- [8] U.S. Bureau of Labor Statistics ??CPI. bls.gov/cpi
Educational content on this page is original prose written for MODOO. Material referenced from Wikipedia is used under the CC BY-SA 4.0 license.