Savings
CD Calculator
CD calculator: see what a certificate of deposit earns over its term — principal, rate, and compounding — before you lock your money in.
2026 Statutory Rates
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Compound Interest Calculator
Forecast exponential investment returns or plan target savings goals. Toggle between "Grow My Money" to project future wealth and "Reach a Goal" to solve for required monthly savings or timeline.
Quick Answer: Compound interest generates exponential financial growth because interest is earned not only on your original principal deposit, but also on all accumulated interest from preceding periods. The future value formula for compound interest with regular periodic contributions is FV = P · (1 + r/n)^(n·t) + PMT · [((1 + r/n)^(n·t) - 1) / (r/n)], where P is principal, r is nominal annual interest rate, n is compounding frequency, t is time in years, and PMT is periodic payment. For an initial deposit of $10,000 invested at 7.00% annual return over 30 years with annual compounding and $0 additional contributions, your total future value reaches exactly $76,122.55—generating $66,122.55 in pure interest gains on a $10,000 investment. In Goal Mode, solving for the monthly savings needed to reach a target FV follows the ordinary annuity formula PMT = [FV - PV · (1 + r/12)^m] ÷ [((1 + r/12)^m - 1) ÷ (r/12)]. For example, reaching a $10,000 goal in 24 months at 4.0% APY ($0 starting) requires saving exactly $400.92 per month.
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Last reviewed: October 2026
Calculation Methodology: Compound Interest Calculator
Mathematical Formula
Grow: FV = P(1 + r/n)^(nt) + PMT[((1 + r/n)^(nt) - 1)/(r/n)] | Goal: PMT = [FV - PV(1+r)^m] ÷ [((1+r)^m - 1)/r]
1. Grow My Money Mode: Compounded future balance equals initial principal accumulated under discrete compounding periods plus the future value of an ordinary annuity of monthly additions.
2. Reach a Goal Mode (Conventions): Monthly interest rate r = APY ÷ 12. Contributions are modeled as an ordinary annuity (end-of-month deposits).
3. Time-to-Goal Solver: Solves for exact compounding periods m = ln[(FV·r + PMT)/(PV·r + PMT)] ÷ ln(1 + r). The engine reports the ceiling month ⌈m⌉ along with the exact accumulated balance at that ceiling month.
Mathematical Principles & Modeling Conventions
- Goal Mode Conventions: Monthly interest rate equals APY ÷ 12. Contributions are credited at the end of each monthly period (ordinary annuity). Time-to-goal displays the integer ceiling month with the exact balance accumulated at that final month.
- Compound Frequency Impact: More frequent compounding (e.g. daily vs annual) produces higher effective yields for the same nominal annual percentage rate (APR) due to faster interest capitalization.
- Tax & Inflation Exclusions: Unless sheltered in a tax-advantaged retirement account (such as a Roth IRA or 401(k)), earnings are subject to annual ordinary income tax, which moderates effective long-term compounding.
Figures illustrate mathematical compounding. Market returns fluctuate over time; cash yields are subject to Federal Reserve monetary policy changes.
Verified Worked Example (Benchmark)
Primary Mathematical Verification Benchmarks:
Grow Mode Benchmark — Long-Term Growth ($10,000 Initial, 7.0% Return, 30 Years, Annual Compounding):
Formula: $10,000 × (1 + 0.07)30 = $10,000 × 7.61225504.
Future Value: $76,122.55 (Pure interest earned: $66,122.55).
Formula: $10,000 × (1 + 0.07)30 = $10,000 × 7.61225504.
Future Value: $76,122.55 (Pure interest earned: $66,122.55).
Goal Benchmark A — Required Monthly Savings ($10,000 Goal, 24 Months, 4.0% APY, $0 Starting):
Monthly Rate r: 0.04 ÷ 12 = 0.00333333 · Annuity factor: ((1 + r)24 − 1) ÷ r = 24.942888.
Required Monthly Contribution: $10,000 ÷ 24.942888 = $400.92/mo.
Monthly Rate r: 0.04 ÷ 12 = 0.00333333 · Annuity factor: ((1 + r)24 − 1) ÷ r = 24.942888.
Required Monthly Contribution: $10,000 ÷ 24.942888 = $400.92/mo.
Goal Benchmark B — Time to Reach Goal ($300/mo at 4.0% APY Toward $10,000 Goal, $0 Starting):
Formula: ln[(10,000 × 0.04/12 + 300) ÷ 300] ÷ ln(1 + 0.04/12) = 31.66 months.
Display Ceiling Month: 32 Months · Balance at Month 32: $10,112.94.
Formula: ln[(10,000 × 0.04/12 + 300) ÷ 300] ÷ ln(1 + 0.04/12) = 31.66 months.
Display Ceiling Month: 32 Months · Balance at Month 32: $10,112.94.
Goal Benchmark C — Target with Initial Seed ($25,000 Goal, 36 Months, 5.0% APY, $1,000 Starting):
Initial principal growth: $1,000 × (1 + 0.05/12)36 = $1,161.62 · Net goal remaining: $23,838.38.
Annuity factor: ((1 + 0.05/12)36 − 1) ÷ (0.05/12) = 38.788193.
Required Monthly Contribution: $23,838.38 ÷ 38.788193 = $615.13/mo.
Initial principal growth: $1,000 × (1 + 0.05/12)36 = $1,161.62 · Net goal remaining: $23,838.38.
Annuity factor: ((1 + 0.05/12)36 − 1) ÷ (0.05/12) = 38.788193.
Required Monthly Contribution: $23,838.38 ÷ 38.788193 = $615.13/mo.
Primary Statutory Sources & Authorities
- Federal Reserve Board Regulation DD (Truth in Savings) — Statutory calculation formulas for Annual Percentage Yield (APY) and compounding disclosure standards.
- FDIC National Deposit Rates and Limits — Official national benchmarks for high-yield savings accounts, money market accounts, and certificates of deposit.
Frequently Asked Questions
Primary source guidance on rules, formulas, and regulations.
Simple interest is calculated strictly on the original principal balance throughout the duration of the deposit or loan (I = P · r · t). Compound interest calculates returns on both the original principal balance and the accumulated interest from prior periods, leading to exponential geometric growth over time.
The more frequently interest compounds, the faster your investment grows. Compounding daily generates slightly higher returns than compounding monthly, and monthly generates more than annually, because earned interest begins accruing additional interest sooner. For example, $10,000 at 7% over 10 years yields $19,671.51 with annual compounding versus $20,136.18 with daily compounding.
The Rule of 72 is a quick mental math shortcut to estimate the number of years required to double your money at a fixed annual interest rate. Divide 72 by the annual interest rate: at an 8% return, your money doubles in approximately 9 years (72 ÷ 8 = 9). At a 6% return, it doubles in approximately 12 years (72 ÷ 6 = 12).
To save $5,000 in 3 months (approximately 13 weeks), you need to save $384.62 per week ($5,000 ÷ 13 weeks). If calculated across 12 calendar weeks, you need to save $416.67 per week. On a monthly basis, this equals setting aside $1,666.67 per month. Over such a short 3-month window, interest earned in a high-yield savings account is modest ($25 to $35), so success relies almost entirely on regular weekly cash deposits.
Yes, but it requires an aggressive savings rate of $3,333.33 per month, which breaks down to $769.23 per week or approximately $109.89 per day. If depositing into a high-yield savings account at 4.0% APY, compound interest will contribute approximately $67 in interest, reducing your required personal deposit to $3,311.23 per month.
Yes. Saving $10,000 in 6 months requires setting aside $1,666.67 per month, or $384.62 per week ($54.95 per day). Deposited into a high-yield savings account at 4.0% APY, compound growth earns roughly $117 in interest over the half-year period, lowering your required monthly contribution to $1,647.17.
In a 3-month window there are 6 biweekly pay periods. To reach $6,000 across 6 paychecks, you must save exactly $1,000.00 per biweekly paycheck ($6,000 ÷ 6 = $1,000). If your employer pays on an alternating 26-pay-period schedule that captures 7 checks in a quarter, your requirement drops to $857.14 per paycheck.
Yes. Reaching a $3,000 goal in 3 months requires saving exactly $1,000.00 per month. On a weekly basis, this equals $230.77 per week ($3,000 ÷ 13 weeks) or approximately $32.97 per day.
To accumulate $1,000,000 in 10 years (120 months) starting from $0: In a diversified stock market index fund earning an average 7.0% annual return (compounded monthly), you need to save $5,777.69 per month ($69,332 per year). Across 10 years, your direct deposits will total $693,323, while compound interest generates $306,677 in growth. In a conservative 4.0% cash savings account, you would need to save $6,839.88 per month.
If you save $1,000 per month for 30 years (360 months) at a 7.0% average annual return compounded monthly, your balance will grow to $1,219,971.00 ($1.22 million). You will have deposited $360,000 in personal savings, while compound interest generates $859,971 in pure growth—more than 2.3 times your original investment. At a conservative 4.0% APY cash rate, you will accumulate $694,049.40 ($334,049 in interest).
The $27.39 rule is a popular daily budgeting heuristic to save $10,000 in exactly one calendar year. Dividing $10,000 by 365 days equals $27.397, rounded to $27.39 per day. By automating a daily transfer of $27.39 (or $191.73 once per week), you accumulate $10,000 by the end of year one.
Yes. Saving $500 per month equals $6,000 per year, which represents 8% to 10% of the median US individual gross income and approaches the annual IRA contribution limit ($7,000 in 2026). Over a 30-year working career at a 7.0% average annual stock market return, saving $500 monthly compounds into $609,985.50 ($180,000 contributed plus $429,985 in pure compound growth).
A lump sum of $10,000 left to compound untouched for 5 years grows to: $12,209.97 at a 4.0% APY high-yield savings rate ($2,210 earned); $14,176.25 at a 7.0% balanced market return ($4,176 earned); and $16,453.09 at a 10.0% historical S&P 500 equity return ($6,453 earned). You can model custom monthly deposits and compounding frequencies using our interactive Grow My Money mode above.