Interest Calculator β Simple vs Compound, Compared
Enter a principal, an annual rate, and a time period to see the simple interest and the total β plus a side-by-side comparison with annual compounding on the exact same inputs.
Your details
Advanced options β contributions, tax and inflation
Contributions, tax on interest and inflation are already included in the result with their default values β open Advanced options to change them.
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Your interest breakdown
- Simple and compound interest earn the same in year one β $800 on $10,000 at 8%. From year two they diverge: over 5 years the gap is already $693, and it keeps growing every year after.
- Judge interest in real terms: 8% nominal with 5% inflation is only (1.08/1.05) – 1 = 2.86% real. The true wealth formula is real rate = (1 + nominal) / (1 + inflation) – 1, after tax.
- Compounding frequency changes the compound side only: this page uses annual compounding as the baseline, and more frequent compounding earns slightly more than the annual figure shown.
Simple vs compound, year by year
The sky-blue line is simple interest (straight line), the orange curve is compound interest (curves upward) β both on your exact inputs. It redraws live as you type.
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How it works
Three steps from your inputs to the full comparison.
Enter principal, rate, time
Type the amount, the annual rate, and the years β decimals allowed.
We compute simple interest
SI = P Γ R Γ T Γ· 100, plus the total you receive.
See the compound comparison
The same inputs with annual compounding β and exactly how much extra it earns.
That, in one line, is how to calculate interest on this page: I work out the simple interest on the original principal first, then rebuild the same inputs with compounding so you can see exactly what the compounding adds. When I check a bank offer or a loan quote, this is the order I use β simple figure first as the honest baseline, compound figure second as the reality check.
The math behind the interest
Simple interest is always computed on the original principal, so it grows in a straight line. Compound interest is computed on the growing balance, so each year’s interest earns interest of its own:
Every interest formula on this page is a rearrangement of these two. If you remember nothing else, remember that simple interest is always principal Γ rate Γ time β every other version, including the compound one, just changes what the rate is applied to.
Worked example β $10,000 at 8% for 5 years: SI = 10,000 Γ 8 Γ 5 Γ· 100 = $4,000 (total $14,000). Compound: 10,000 Γ 1.08β΅ = $14,693.28, so CI = $4,693.28 β compounding earns $693.28 extra on identical inputs.
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The details that separate a rough guess from a trustworthy estimate.
Simple interest calculator: the mode I lead with
I built this interest calculator to answer the simple question first, because most everyday interest β a short loan, a deposit under a year, interest on an overdue invoice β is simple interest. In this mode the interest is charged only on the original principal, never on interest already earned, so the amount grows by exactly the same slice every year.
That is the whole simple interest formula: I = P Γ r Γ t, where P is the principal, r is the annual rate as a decimal, and t is the time in years. Worked example β I put $5,000 at 6% for 3 years: I = 5,000 Γ 0.06 Γ 3 = $900, so I get back $5,900. Notice the rhythm: exactly $300 of interest lands every year β year 1, year 2 and year 3 are identical, which never happens with compounding.
Fractional time works the same way, which is why I allow decimals in the time field. $2,400 at 5% for 6 months is t = 0.5: I = 2,400 Γ 0.05 Γ 0.5 = $60. Whenever I need a quick, honest estimate β what a sum earns, what a short loan costs β this is the mode I start with, and the compound comparison below it is there to show what changes when interest starts earning interest too.
Where do I meet simple interest in real life? On many car and personal loans, on Treasury bills, on the coupon of most bonds, and in the fine print of late-payment penalties. The results panel above is already in this mode: the big number is your simple interest, and the compound rows underneath exist purely as a comparison on the same inputs β same principal, same rate, same years.
Year-by-year schedule
Balance at each year-end, at the selected compounding frequency. The compound balance includes any regular contributions from Advanced options.
| Year | Simple balance | Compound balance | Gap |
|---|
The complete guide to interest
Everything about simple vs compound interest β the formulas, compounding frequency, and where each type shows up in real life.
Simple vs compound: the two formulas
Simple interest pays only on the original principal: SI = P x R x T / 100. $10,000 at 8% for 5 years earns 10,000 x 8 x 5 / 100 = $4,000, exactly $800 every year, forever. The growth is a straight line.
Compound interest pays on principal plus accumulated interest: A = P x (1 + R/100)^T. The same $10,000 at 8% for 5 years becomes 10,000 x 1.08^5 = 10,000 x 1.46933 = $14,693.28 β interest of $4,693.28, already $693 more than simple. Over 20 years the gap explodes: $16,000 of simple interest vs $36,610 of compound interest (totals $26,000 vs $46,610).
The divergence is back-loaded: in year 1 they are identical (both $800). By year 10, compound earns $1,599 that year versus simple’s flat $800. Time is the multiplier β compounding rewards patience exponentially, which is why starting retirement savings at 25 versus 35 matters more than the amounts involved.
The crossover point β when compound interest earned in a single year exceeds the total simple interest β is instructive. At 8%, simple earns $800/year always. Compound earns 8% of a growing base: year 10 earns $1,599, year 15 earns $2,346, year 20 earns $3,445. By year 20, one year of compounding ($3,445) exceeds four years of simple interest. The schedule table above shows this acceleration year by year β watch the “Gap” column widen.
Compounding frequency: how often matters
The nominal rate is not the whole story β how often interest compounds changes the outcome. The general formula: A = P x (1 + R/(100 x n))^(n x T), where n is compounds per year. $10,000 at 8% for 20 years:
| Frequency | n | Final amount | Extra vs annual |
|---|---|---|---|
| Annual | 1 | $46,609.57 | β |
| Half-yearly | 2 | $48,010.21 | +$1,400.64 |
| Quarterly | 4 | $48,754.39 | +$2,144.82 |
| Monthly | 12 | $49,268.03 | +$2,658.46 |
| Semimonthly | 24 | $49,398.71 | +$2,789.14 |
| Biweekly | 26 | $49,408.80 | +$2,799.23 |
| Weekly | 52 | $49,469.46 | +$2,859.89 |
| Daily | 365 | $49,521.64 | +$2,912.07 |
Notice the diminishing returns: going annual to quarterly adds $2,145, but quarterly to daily adds only $767. The mathematical limit is continuous compounding: P x e^(RT/100) = 10,000 x e^1.6 = $49,530.32 β daily compounding is already 99.98% of the way there. Try the frequency buttons above to see this live.
Banks quote the effective annual rate (EAR) to make frequencies comparable: EAR = (1 + R/(100 x n))^n β 1. An 8% nominal rate compounded monthly is really (1.0066667)^12 β 1 = 8.30% effective. When comparing FDs or loans, always compare EAR, not nominal rates.
The advertising trap: Bank A offers “8% compounded quarterly,” Bank B offers “7.9% compounded monthly.” Nominal says A wins. EAR says: A = (1.02)^4 β 1 = 8.24%, B = (1 + 0.079/12)^12 β 1 = 8.19% β A still wins, but by 0.05%, not 0.10%. Now try Bank C at “8.1% simple annual”: EAR = 8.10% flat β which loses to A’s 8.24% despite the higher nominal number. Nominal rates are marketing; EAR is truth.
Where simple interest still rules
Simple interest is not obsolete β it dominates short-term lending. Car loans, personal loans, and many EMIs use simple (flat) interest over the loan term because the tenure is short and the math must be transparent. India’s PPF technically compounds annually. US Treasury bills and most bonds pay simple coupon interest on face value.
The rule of thumb: under 1β2 years, the difference is negligible β $10,000 at 8% for 1 year is $800 either way. Simple interest wins on clarity for short horizons; compounding wins on growth for long ones. Lenders choose based on which side of that trade benefits them: credit cards compound daily (great for the bank), while your savings account might compound quarterly.
India’s PPF is a fascinating hybrid: interest compounds annually, but it’s calculated on the lowest balance between the 5th and month-end β deposit before the 5th to maximize it. At 7.1%, $150,000/year for 15 years becomes roughly $3.80 million (annuity: 150,000 x ((1.071^15 β 1)/0.071)). Miss the 5th-of-month cutoff consistently and you silently forfeit thousands.
EPF compounds monthly on (employer + employee) contributions β the closest most salaried Indians get to true monthly compounding on autopilot. The lesson: frequency is often chosen for you; your lever is the rate and the principal, not the n.
Rule of 72 for quick mental math: divide 72 by the rate to get doubling time. At 8% compounded annually, money doubles every 9 years (72/8). At 8% simple interest, doubling takes 100/8 = 12.5 years. The 3.5-year gap is pure compounding magic.
Loan interest, costed the simple way
When I use this page as a loan interest calculator, I am costing the slice of loan interest I can do on the back of an envelope: a single sum, one rate, one term, no monthly schedule. Plenty of short-term lending really is priced that way. Say I borrow $15,000 at 7% for 4 years on simple interest: I = 15,000 Γ 0.07 Γ 4 = $4,200 of interest, $19,200 repaid in total β the equivalent of a flat $400 a month, of which $87.50 is interest.
This is also how I sanity-check any simple interest loan calculator quote: if the lender’s total interest is far from P Γ r Γ t, something else β fees, insurance, a different day-count β is hiding in the quote. But I am honest about the limit: most car and personal loans in the US actually amortize, with a payment that blends principal and interest month by month. For that math I switch to the Loan Calculator for the payment itself and the Amortization Calculator to see the balance fall payment by payment. Simple interest tells me what a loan costs; amortization tells me how it is paid off.
Solving for the rate: turn the formula around
Half the questions I get are really an interest rate calculator question in disguise: “how do I find the interest rate when all I can see is that my money grew?” The simple interest formula rearranges cleanly. If I know the interest earned, the rate is r = I Γ· (P Γ t). If I only know the start and end amounts, I use r = (A Γ· P β 1) Γ· t. That is how to calculate interest rate from figures you already have, with no guessing.
Worked example: I deposit $8,000 and three years later it is worth $9,200. The interest is $1,200, so r = 1,200 Γ· (8,000 Γ 3) = 5% a year, simple. If that growth had come from annual compounding instead, the same rearrangement with a cube root β r = (A Γ· P)1/t β 1 β gives 4.77%: compounding reaches the same total from a slightly lower rate, which is exactly why I always ask which basis a quoted rate uses before I compare two offers.
Interest by the month, and by the day
I often want the monthly figure rather than the yearly one, and the same formula rescales: used as a monthly interest calculator, simple interest per month is just P Γ r Γ· 12. On $12,000 at 6% that is $60 a month, $720 over a full year. If the account compounds monthly instead, the year pays a little more β $740.13 β because each month’s interest starts earning its own. And if you want to calculate interest rate per month from an annual quote, divide by 12 the same way: 6% a year is 0.5% a month.
Daily works identically: used as a daily interest calculator, simple interest per day is P Γ r Γ· 365 β $1.97 a day on that same $12,000 at 6%, or $177.53 across 90 days. I use the daily figure for overdue invoices and short settlements, where interest genuinely accrues by the day. One boundary I keep in mind: this is simple daily accrual. Daily compounding, where each day’s interest joins the balance, is a different beast and lives on the Compound Interest Calculator.
The real-world cost of compounding: credit cards
Compounding cuts both ways. A credit card at 3% monthly (36% nominal APR) compounds to an effective (1.03)^12 β 1 = 42.6% per year. A $50,000 balance making only minimum payments can take 10+ years and cost more in interest than the original purchase. This is why financial advisors scream about high-interest debt: the same exponential curve that builds wealth destroys it in reverse.
Compare: $50,000 invested at 12% compounded annually for 10 years becomes 50,000 x 1.12^10 = $155,292. The same $50,000 owed at 36% nominal (monthly compounding) for 10 years becomes 50,000 x (1.03)^120 = $1,735,549 β thirty-five times the principal. Never pay credit-card interest while holding investments earning less. The spread is a guaranteed loss.
The minimum-payment trap quantified: $50,000 at 3%/month with a 5% minimum payment ($2,500 floor). Month 1: interest $1,500, payment $2,500, principal drops $1,000. It takes over 4 years and ~$22,000 in interest to clear β and that’s without new spending. Add $5,000/month in new charges and the balance grows forever: interest ($1,500+) exceeds the minimum. This is the debt spiral β the only exit is paying far above minimum.
Taxes and inflation: the silent partners
Interest earned is usually taxable β and taxes compound against you. $10,000 at 8% for 20 years is $46,610 pre-tax. At 30% tax on interest each year (roughly), the effective rate drops to 5.6%, giving 10,000 x 1.056^20 = $29,735 β you lose over a third to tax drag. Tax-advantaged accounts (PPF, EPF, 401(k), Roth IRA) exist precisely to shield compounding from this drag.
Inflation is the other partner: 8% nominal with 5% inflation is only (1.08/1.05) β 1 = 2.86% real. Always judge interest in real terms β a 7% FD during 6% inflation barely preserves purchasing power. The true wealth formula is: real rate = (1 + nominal)/(1 + inflation) β 1, after tax.
Roth vs traditional is a compounding question in disguise. Contribute $10,000 pre-tax to a traditional account at 8% for 30 years: 10,000 x 1.08^30 = $100,627, then pay 30% tax = $70,439. Or pay 30% tax now ($7,000) into a Roth: 7,000 x 1.08^30 = $70,439 tax-free. Identical β if your tax rate never changes. Roth wins when your future rate is higher; traditional wins when it’s lower. The compounding itself doesn’t care about the wrapper.
Putting it together: the savings hierarchy
Where should each dollar go? First, kill high-interest debt (anything above ~10%): the guaranteed “return” of avoiding 36% credit-card compounding beats every investment. Second, build an emergency fund (6 months expenses) in a liquid account β return matters less than access. Third, max tax-advantaged compounding (PPF/EPF/401(k)): decades of untaxed compounding is the highest-leverage move available. Fourth, taxable investing for the remainder.
The order matters more than the amounts: $10,000/year for 30 years at 10% is 10,000 x ((1.10^30 β 1)/0.10) = $1,644,940. Start 10 years late (20 years): $572,750. The late starter must save 2.9x more per year to catch up. Compounding rewards the early β start now, optimize later.
The cost of waiting in stark terms: invest $10,000/year from age 25 to 35 (10 years, then stop) at 10%: 10,000 x ((1.10^10 β 1)/0.10) = $159,374 at 35, then compounding untouched to 65: 159,374 x 1.10^30 = $2,780,000. Start at 35 and invest $10,000/year for 30 straight years: $1,644,940. The early starter contributed one-third the money ($100,000 vs $300,000) and ended with 69% more. Time beats money β every year of delay has a price tag.
Compounding is interest on interest. In year one, both methods earn the same ($800 on $10,000 at 8%). From year two onward they diverge:
- Simple keeps earning $800 every year β the principal never changes.
- Compound earns 8% on $10,800 in year two, then on $11,664 in year three β the base keeps growing.
- Over 5 years the gap is $693; over 20 years it becomes dramatic: $16,000 of simple interest vs $36,610 of compound interest (totals $26,000 vs $46,610) on the same $10,000.
This is why long-term savings (retirement funds, PPF, SIPs) compound, and why lenders prefer compounding for long loans β time magnifies the difference.
Simple interest is not just a teaching tool β it is the actual convention in several real products:
- Short-term loans β personal loans, auto loans, and many business loans quote simple interest over the loan term.
- Fixed deposits (short tenures) β some banks pay simple interest on deposits under a year.
- Late fees and penalties β statutory interest on overdue amounts is usually simple.
- Quick estimates β for horizons under a year, the SI/CI gap is tiny, so simple interest is a fine mental shortcut.
When a bank advertises “compounded quarterly”, use the compound comparison on this page as the baseline β and remember more frequent compounding earns slightly more than the annual figure shown here.
Daily and monthly interest, and accrued interest
Interest is usually quoted by the year but charged by the day or the month. The gap between the two is where payment timing starts to matter.
Daily interest is the annual rate divided by 365, charged on the balance each day. On $10,000 at 8%, that is $2.19 a day, or $66.67 for a 30-day month at the same rate if the balance never moves β the monthly figure is simply the daily figure accumulated. The distinction starts to matter when the balance moves during the month: on a daily-accrual loan, a payment made on the 5th stops interest accruing on the amount paid for the remaining 25 days, while on a loan that accrues monthly, the same payment may not change that month interest at all. Mortgages and many personal loans accrue monthly; credit cards accrue daily. Knowing which kind a loan is tells you whether paying early in the cycle is worth anything.
Accrued interest is interest that has been earned or owed but not yet paid or posted. A savings account accrues interest daily and posts it monthly; a loan accrues interest from the day the money is drawn, including the days before the first statement. Over five years the accrual method itself changes the total: $10,000 at 8% simple interest earns $4,000 of interest, while the same $10,000 compounded annually earns $4,693.28, because each year interest joins the balance and starts earning in turn. The schedule on this page shows the accrual year by year, so the difference between a rate, a balance and a total can be seen rather than assumed.
Frequently asked questions
Quick answers about simple and compound interest.
What is simple interest?
Simple interest is calculated only on the original principal: SI = P Γ R Γ T Γ· 100. It grows in a straight line because the amount earning interest never changes. On $10,000 at 8% for 5 years, it earns $4,000.
What is compound interest?
Compound interest is calculated on the growing balance β each period’s interest is added to the principal and earns interest itself: A = P Γ (1 + RΓ·100)^T. On $10,000 at 8% for 5 years (annual compounding), it earns $4,693.28 β $693.28 more than simple interest.
Which is better, simple or compound interest?
As an investor you want compound interest (it earns more over time); as a borrower you pay less with simple interest. The gap grows with time and rate β negligible under a year, dramatic over decades. This calculator shows the exact difference for your inputs.
When is simple interest actually used?
Simple interest is the real convention for many short-term loans (personal, auto, business), some short-tenure fixed deposits, and statutory interest on overdue amounts. It is also the standard way to estimate interest mentally for horizons under a year.
Does compounding frequency matter?
Yes. Use the frequency buttons above to compare annual, half-yearly, quarterly, monthly, semimonthly, biweekly, weekly, daily and continuous compounding on your own numbers β more frequent compounding earns slightly more, because interest joins the principal sooner. The effective annual rate (EAR) shown in the results puts every frequency on one comparable footing.
Can I use months instead of years?
Yes β there is a dedicated months box beside the years field. The months are added to the years, so 30 months with 0 in the years field is exactly the same as entering 2.5 years. Decimals in the years field still work too: 0.5 years is 6 months.
How does compounding frequency affect my returns?
More frequent compounding earns slightly more: $10,000 at 8% for 20 years becomes $46,610 annually but $49,268 monthly. Use the frequency buttons above to compare. The gains diminish though β daily beats monthly by only $254 on $10,000 over 20 years.
What is the difference between nominal rate and effective annual rate?
The nominal rate ignores compounding frequency; the effective annual rate (EAR) includes it: EAR = (1 + R/(100 x n))^n β 1. An 8% nominal rate compounded monthly is 8.30% effective. Always compare EARs, not nominal rates, when choosing between FDs or loans.
Is the interest shown before or after tax?
Before tax. Interest income is usually taxable, which drags the effective rate down β at 30% tax, an 8% return compounds at only 5.6%. Tax-advantaged accounts (PPF, EPF, 401(k)) shield compounding from this drag.
What is the difference between simple and compound interest?
Simple interest is charged only on the original principal, so it grows by the same amount every year. Compound interest is charged on the growing balance, so the interest itself earns interest. On $10,000 at 8% for 5 years, simple interest earns $4,000 while annual compounding earns $4,693.28 β and the gap widens every year after that.
How do I work out the interest rate if I know the amount, principal and time?
Rearrange the simple interest formula: r = (A β P) Γ· (P Γ t), or with the interest itself, r = I Γ· (P Γ t). If $8,000 grows to $9,200 in 3 years, the interest is $1,200 and r = 1,200 Γ· (8,000 Γ 3) = 5% a year. The ‘Solving for the rate’ section above walks through the compound version too.
How much interest will I pay?
On a simple-interest loan, I = P Γ r Γ t: borrow $15,000 at 7% for 4 years and you pay $4,200 in interest, $19,200 in total. Most real loans amortize month by month, though, so for the exact monthly payment and a payment-by-payment schedule, use the Loan Calculator and the Amortization Calculator.
How much interest will $10,000 earn in a year?
It depends on the rate and the compounding. At 4% simple interest, $10,000 earns exactly $400 in a year; compounded monthly it earns $407.42. At this page’s default 8%, the same deposit earns $800 simple, or $830.00 with monthly compounding. Enter your own rate above to see both figures side by side.
Is simple interest better for borrowers or for savers?
For borrowers β with simple interest the charge never snowballs, because interest is not charged on interest. Savers and investors are better off with compound interest, which pays them on a growing balance. On $10,000 at 8% over 20 years, a borrower pays $16,000 in simple interest but $36,610 in compound interest β that $20,610 gap is why lenders love compounding and borrowers should prefer simple.
How is daily interest calculated?
Divide the annual rate by 365 and apply it to the balance each day. On $10,000 at 8 percent, daily interest is $10,000 times 0.08 divided by 365, which is $2.19 a day. Over a 30-day month with an unchanged balance that is $65.75, and over a full year it is $800 before compounding. Daily interest matters most on balances that change during the month, because each day balance is charged separately, so a payment made early in the cycle saves more than the same payment made late.
What is accrued interest?
Accrued interest is interest that has built up over time but has not yet been paid or added to the account. On a loan, interest accrues from the day the money is drawn, so the first statement already contains interest for the days before it was printed. On a savings account, interest accrues daily and is usually posted monthly, so the accrued amount is the interest earned since the last posting date. Accrued interest is real money owed or earned; it is only the payment or posting that is still to come.
Why does my statement show interest I have not paid yet?
Because interest accrues continuously while statements are snapshots. The statement prints the interest accrued up to the statement date, including days since the last payment, and the next statement will add the days since this one. On a daily-accrual loan the figure keeps growing by a small amount every day until a payment lands. The statement is not charging interest twice; it is reporting the running total of interest that has accrued and not yet been paid.
Does paying early in the month save interest?
It depends on how the loan accrues. On a daily-accrual loan, yes: a payment made early stops interest accruing on the amount paid for the rest of the cycle, so the same payment saves a little more than one made on the due date. On a monthly-accrual loan, the timing within the month usually makes no difference, because interest for the month is calculated on the balance at a fixed point. Check the loan agreement for daily or monthly accrual before rearranging payment dates, and never pay so early that a payment is missed in the following cycle.
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Disclaimer
Results are mathematical computations for information only β they are not financial advice. Simple interest is computed as P Γ R Γ T Γ· 100 and the comparison uses annual compounding (A = P Γ (1 + RΓ·100)^T). Real products may compound monthly, quarterly, or half-yearly, charge fees, or tax the interest β all of which change the actual amounts. Consult a qualified financial adviser before making investment or borrowing decisions.