Interest Calculator

The Interest Calculator computes earnings or costs from both simple interest (calculated only on the original principal) and compound interest (calculated on principal plus previously accumulated interest). Understanding the difference between these two structures is foundational to every personal finance decision — from choosing a savings account to evaluating a loan's true cost.

Compound interest is what Albert Einstein reportedly called the eighth wonder of the world, and the numbers justify the reverence. A $10,000 investment earning 7% simple interest for 30 years grows to $32,500. The same $10,000 at 7% compounded annually grows to $76,123 — more than double. The difference, $45,123, is the power of earning "interest on interest." Small differences in compounding frequency and rate have large effects over multi-decade horizons.

Where each interest type appears:

• Simple interest: Car loans, some personal loans, Treasury bills, bonds (stated coupon), installment loans, and some savings bonds. Also used in day-count conventions for short-term lending.
• Daily compounding: Most savings accounts, money market accounts, and credit cards. The APY (Annual Percentage Yield) reflects daily compounding while the APR (Annual Percentage Rate) reflects the nominal rate. Per FDIC Truth in Savings rules, banks must disclose both APR and APY so consumers can compare accounts accurately.
• Monthly compounding: Most mortgages, student loans, and home equity loans use monthly compounding. The monthly payment formula is derived from monthly compounding of the stated annual rate.
• Quarterly/annual compounding: Some CDs, I-bonds, and savings products compound quarterly or annually. The less frequent the compounding, the lower the effective yield for a given nominal rate.

Canadian equivalents: in Canada, mortgage interest is legally required to compound semi-annually, not monthly — a regulatory distinction that makes Canadian mortgages slightly less expensive than an equivalent US monthly-compounding product at the same stated rate. The Office of the Superintendent of Financial Institutions (OSFI) governs Canadian mortgage disclosure standards.

The two interest formulas produce dramatically different outcomes, especially over longer time horizons. Both are presented with standard derivations and worked examples using realistic 2025 rates.

The Rule of 72 is a quick mental math shortcut for estimating doubling time: divide 72 by the annual compound interest rate to estimate years to double. At 6%, money doubles in roughly 72 ÷ 6 = 12 years. At 9%, it doubles in ~8 years. This rule has been cited in financial literacy materials by the SEC's financial education resources as one of the most useful quick estimates in personal finance.

This calculator handles both savings scenarios (you earn interest) and loan/debt scenarios (you pay interest). Follow these steps for each use case.

1. Select interest type: Simple or Compound.
   For savings accounts, CDs, and most investment accounts: select Compound. For most car loans and some personal loans: select Simple. If unsure, check your account's Truth in Savings disclosure (savings) or Loan Estimate/Truth in Lending disclosure (loans) — both are legally required to specify the compounding method.
2. Enter principal amount.
   For savings: your initial deposit. For loans: the original loan balance. Example: $50,000 initial deposit in a high-yield savings account.
3. Enter the annual interest rate.
   Use the APR for apples-to-apples comparisons, then let the calculator derive the APY. High-yield savings rates change often, so compare current offers. Online banks and credit unions often pay more than large national banks, and the FDIC's national average savings rate is a small fraction of what top high-yield accounts pay.
4. Select compounding frequency.
   Daily compounding earns more than monthly, which earns more than annual. For the $50,000 deposit at 5.00% over 5 years:
   Annual compounding: $63,814
   Monthly compounding: $64,168
   Daily compounding: $64,201
   The daily-vs-annual difference ($387) is meaningful but not dramatic for a 5-year horizon; it compounds more significantly over 20–30 years.
5. Set the time period.
   Enter years and months. For goal-oriented calculations, use the reverse function: enter your target future value and the calculator shows the required starting principal or required rate to reach that goal.
6. Compare simple vs. compound for a loan scenario.
   $30,000 car loan at 7.50% (try it in our Car Loan Calculator):
   Simple interest (5-year auto loan): Total interest = $30,000 × 7.50% × 5 = $11,250 (stated amount; actual payoff uses amortization)
   Monthly compounding (credit card cash advance at 7.50% — see the Credit Card Interest Calculator): 5-year cost = $43,342 − $30,000 = $13,342
   The compound interest loan costs $2,092 more over 5 years.
7. Model the impact of regular contributions.
   Switch to "regular deposits" mode: $500/month added to the $50,000 at 5.00% compounded monthly for 20 years:
   Starting $50,000 grows to: $136,602
   Monthly $500 contributions total: $205,517
   Combined balance: $342,119 — nearly 3.4× the $152,000 total cash invested.

The Interest Calculator produces a suite of outputs that together give a complete picture of how time, rate, and compounding frequency interact.

Future Value (FV): The total balance at the end of the period, including principal and all accrued interest. This is the primary output for savings and investment planning. For a $10,000 deposit at 6% compounded monthly over 30 years, FV = $60,226 — turning $10,000 into six times the original investment without any additional contributions.

Total Interest Earned/Paid: FV minus the initial principal (and minus any additional contributions for multi-deposit scenarios). This separates how much came from your own money versus the money the interest rate generated. Over 30 years at 6%: $10,000 principal generates $50,226 in interest — a 5:1 interest-to-principal ratio.

APY vs. APR: The calculator surfaces both the nominal rate (APR) you input and the effective annual rate (APY) that results from your chosen compounding frequency. When evaluating savings accounts, always compare APYs, not APRs. Per FDIC Truth in Savings rules, financial institutions must prominently disclose APY on all deposit products, precisely because APY is the standardized comparison metric.

Year-by-Year Growth Table: Shows the balance at the end of each year, the interest earned that year, and the cumulative interest to date. This table makes the exponential nature of compounding visible — in the early years, interest increments are modest; in later years they accelerate dramatically. On a $50,000 account at 6% compounded monthly: year 1 interest = $3,084; year 10 interest = $5,465; year 20 interest = $9,790; year 30 interest = $17,527. The annual interest in year 30 alone exceeds the original investment in year 1 — a visceral illustration of compound growth.

Simple vs. Compound Comparison Chart: Displays both trajectories on the same timeline. The gap widens with time: at year 5 the difference is modest; at year 30 the compound result is typically 2–4× the simple interest result for rates in the 5–8% range. This comparison is most useful for borrowers evaluating whether a stated "simple interest" loan is genuinely cheaper than a compound alternative at the same nominal rate — it is, particularly for loans paid off before maturity.

• Choose daily-compounding high-yield savings accounts for emergency funds. Online banks currently offer 4.75–5.10% APY on savings accounts — 10× the national average. On a $30,000 emergency fund, the difference between a national bank's 0.45% and an online bank's 5.00% is $1,665/year in additional interest. Over 5 years, that gap compounds to approximately $8,900 in foregone earnings. FDIC insurance covers up to $250,000 per depositor per institution — online banks carry the same protection as traditional banks.
• Use the Rule of 72 as a reality check on investment projections. Before trusting any financial projection, apply Rule of 72. At 8% annual return, money doubles every 9 years (72 ÷ 8). At 12%, every 6 years. If a salesperson's projection shows your money doubling in 4 years, that implies a ~18% guaranteed return — an immediate red flag. The Rule of 72 is your fastest fraud detector for unrealistic investment claims, per guidance from the SEC's investor protection resources.
• Pay off compound-interest debt before building savings in lower-yield accounts. If you have $10,000 in a savings account earning 5% and $10,000 in credit card debt at 22%, the net result is a 17% annual loss on the matched capital. Pay off the credit card first — the guaranteed "return" from eliminating 22% compound interest exceeds any available savings or investment rate. Only after high-interest debt is eliminated does building a savings/investment position make mathematical sense.
• Understand the difference between APR and APY when comparing loans. Lenders quote APR; savings institutions quote APY. For loans, a lower APR is better; for savings, a higher APY is better. Never compare a loan's APR to a savings account's APY — they measure different things. When comparing two loans, always use APR (which includes fees). When comparing two savings products, always use APY (which includes compounding). This confusion costs consumers billions annually in missed comparisons.
• Reinvest interest income immediately to maximize compound growth. Many certificates of deposit pay interest monthly or at maturity; if the interest is not reinvested (swept back into the CD or another compounding account), you forfeit the compounding benefit and effectively earn simple interest. An $80,000 CD at 5.00% over 5 years earns $22,081 with compound reinvestment versus $20,000 with simple interest — a $2,081 difference that grows more significant with larger balances and longer terms.
• Start compound interest working as early as possible. A $5,000 investment at age 25 at 7% compounded annually grows to $74,872 by age 65 (40 years). The same $5,000 invested at age 35 grows to $37,072 by age 65 (30 years). A 10-year head start more than doubles the final result. The SEC's compound interest calculator demonstrates that time is the single most powerful variable in the compound interest equation — more powerful than rate within any realistic range.

The difference between simple and compound interest is invisible in year one and enormous by year thirty. Here is $10,000 at a 7% annual rate under both methods:

By year 30, compounding has produced $45,000 more than simple interest from the identical starting point — and that gap widens with time, rate, and compounding frequency. Daily compounding at the same nominal rate lifts the final balance further still (the calculator above lets you compare daily, monthly, and yearly frequencies directly). This same mechanism working against you is why credit card APR compounds so painfully, and working for you is the engine behind systematic monthly investing and dividend reinvestment.

While this calculator handles compound interest in full detail, the simple interest formula is where most people start — and where many loan agreements actually work. Simple interest is calculated only on the original principal, never on accumulated interest. That makes it predictable, linear, and easy to reverse-engineer.

The formula has two standard forms:

Where I = total interest, P = principal (starting amount), r = interest rate as a decimal, t = time in years, and n = number of periods.

Simple Interest: Worked Examples

Example 1 — Car loan (borrower paying simple interest). You finance a $22,000 car at 6.0% annual simple interest for 4 years.

• I = $22,000 × 0.06 × 4 = $5,280 total interest
• Total repayment = $22,000 + $5,280 = $27,280
• Monthly payment = $27,280 ÷ 48 = $568.33

Example 2 — Savings account (lender earning simple interest). You deposit $8,000 at 4.5% simple interest for 2 years.

• I = $8,000 × 0.045 × 2 = $720 total interest
• End balance = $8,720
• Compare: $8,000 at 4.5% compounded monthly for 2 years = $8,754 — $34 more from compounding

Example 3 — Six-month personal loan. $5,000 at 12% APR for 6 months (t = 0.5 years).

• I = $5,000 × 0.12 × 0.5 = $300 total interest
• Total repayment = $5,300

Which Financial Products Use Simple Interest?

Most auto loans and many personal loans use simple interest — the interest charge is based solely on the remaining principal balance, and it decreases as you pay down the loan. U.S. Treasury bills also use a simple interest (discount) structure. By contrast, credit cards, most mortgages, and savings accounts use compound interest, where interest accrues on both principal and previously earned interest. As a borrower, simple interest costs you less over time; as a saver, you want compound interest working for you instead.

Most loan products — including auto loans, student loans, and mortgages — accrue interest daily, even when payments are monthly. Understanding the daily rate is essential for two decisions: comparing lenders accurately, and calculating exactly how much interest you save by making an extra payment.

The daily interest calculation is straightforward:

Auto loan example. You have a $28,000 car loan at 7.0% APR. Your bank accrues interest daily on the remaining balance.

• Daily rate = 7.0% ÷ 365 = 0.01918% per day
• Daily interest charge = $28,000 × 0.0001918 = $5.37/day
• Interest accrued in a 30-day month = $5.37 × 30 = $161.10

If you make your payment 10 days early, you save approximately $53.70 in interest for that period — and your extra payment reduces the principal immediately, lowering every future day's accrual.

Student loan example. Federal direct loans for undergraduates carry a 6.39% rate for 2025–2026. On a $35,000 balance:

• Daily interest = $35,000 × (0.0639 ÷ 365) = $6.12/day
• During a 6-month grace period: $6.12 × 183 days = $1,120 in accrued interest that capitalizes if unpaid

Why 365 vs. 360? Most consumer loans divide by 365. Some commercial loans and certain mortgage products use a 360-day year (called the "banker's year"), which slightly raises your effective rate. Always confirm which divisor your lender uses — it can add up on large balances.

For credit cards, the daily periodic rate is your APR ÷ 365, multiplied by your average daily balance. Cards compound daily on unpaid balances, which is why carrying a $5,000 balance at 24% APR generates about $3.29/day in interest that then accrues its own interest the following day. The Credit Card Interest Calculator shows exactly how this compounds over your payoff timeline.

An interest-only loan is one where your monthly payment covers only the interest charge for a set period — no principal is paid down. At the end of the interest-only term, payments jump sharply as the full principal must be amortized over the remaining loan life. This structure appears in some adjustable-rate mortgages (ARMs), construction loans, commercial real estate financing, and short-term bridge loans.

The interest-only monthly payment formula is simple:

Example — Interest-only ARM. You take a 30-year ARM at 6.50% with a 5-year interest-only period on a $400,000 loan.

• Interest-only payment (years 1–5): ($400,000 × 0.065) ÷ 12 = $2,167/month
• After year 5, principal must amortize over 25 years at the new rate
• If rate adjusts to 7.5% on $400,000 remaining: new payment ≈ $2,946/month — a $779 increase

The interest-only structure saves $287/month in the short term but costs roughly $56,760 more in total interest — because the principal never shrinks during those five years. For buyers who plan to sell before the IO period ends, or who invest the payment difference at a higher return, it can still make financial sense. For those expecting income growth, it can ease early cash flow pressure. The key is entering this structure with eyes open on the payment reset risk.

Use the calculator above to model different principal amounts and rates. For the full payment schedule including the amortization phase, the Complete Loan Calculator generates a complete table.