Compound Interest Calculator
Compound interest is interest earned on both the initial principal and the interest already accumulated, calculated with the formula A = P(1 + r/n)^(nt). This calculator projects how savings or investments grow over time and shows a year-by-year breakdown of balance and total interest earned.
Compound Interest Calculator
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Formula: FV = P(1 + r/n)^(nt) + PMT × [(1 + r/n)^(nt) - 1] / (r/n)
Worked example — Future Value: $691,150 | Contributed: $190,000 | Interest: $501,150 (264%)
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor · Editorial policy
How is compound interest calculated?
FV = P(1 + r/n)^(nt) + PMT × [(1 + r/n)^(nt) - 1] / (r/n)
Where FV = Future Value, P = Principal (initial investment), r = Annual interest rate (decimal), n = Compounding frequency per year, t = Time in years, PMT = Regular periodic contribution. The first term calculates growth of the initial lump sum, and the second term (future value of an annuity) calculates growth from regular contributions.
How do you calculate compound interest step by step?
Example 1: Retirement Savings Growth
Problem:You invest $10,000 today and add $500/month at 7% annual return for 30 years. How much will you have?
Solution:FV of initial $10,000 = $10,000 × (1 + 0.07/12)^(12×30) = $10,000 × 8.116 = $81,165 FV of $500/month = $500 × ((1.005833)^360 - 1) / 0.005833 = $500 × 1,219.97 = $609,985 Total = $81,165 + $609,985 = $691,150 Total contributed = $10,000 + $500 × 360 = $190,000 Interest earned = $691,150 - $190,000 = $501,150
Result:Future Value: $691,150 | Contributed: $190,000 | Interest: $501,150 (264%)
Example 2: Early vs Late Start Comparison
Problem:Person A starts at 25, invests $300/month for 40 years. Person B starts at 35, invests $300/month for 30 years. Both earn 7%.
Solution:Person A (40 years): FV = $300 × ((1.0058333)^480 - 1) / 0.0058333 = $300 × 2,624.81 = $787,444 Total contributed: $300 × 480 = $144,000 Interest: $643,444 Person B (30 years): FV = $300 × ((1.0058333)^360 - 1) / 0.0058333 = $300 × 1,219.97 = $365,991 Total contributed: $300 × 360 = $108,000 Interest: $257,991
Result:10 years earlier = $421,453 MORE (2.15x) with only $36,000 extra invested
What else do people ask about compound interest?
What is compound interest and how does it work?
Compound interest is interest calculated on both the initial principal AND the accumulated interest from previous periods — essentially 'interest on interest.' This creates exponential growth over time, which Albert Einstein reportedly called 'the eighth wonder of the world.' Unlike simple interest (which only earns interest on the original principal), compound interest accelerates wealth building. For example, $10,000 at 7% simple interest earns $700/year forever. With compound interest, year 1 earns $700, year 2 earns $749, year 3 earns $801, and by year 20 you're earning $2,530 in interest that year alone. The more frequently interest compounds (daily vs monthly vs annually), the faster your money grows.
How does compounding frequency affect returns?
More frequent compounding produces higher returns because interest starts earning interest sooner. For $10,000 at 7% over 20 years: Annual compounding = $38,697. Quarterly = $39,365. Monthly = $39,602. Daily = $39,739. The difference between annual and daily compounding is $1,042 — meaningful but not dramatic. The biggest jump is from annual to monthly compounding. This is why savings accounts advertise APY (Annual Percentage Yield, which accounts for compounding) rather than the nominal rate. A 7% nominal rate with monthly compounding has an effective APY of 7.229%. For most practical purposes, monthly and daily compounding produce very similar results.
What is the Rule of 72 in compound interest?
The Rule of 72 is a quick mental math shortcut to estimate how long it takes for an investment to double at a given annual rate of return. Simply divide 72 by the annual interest rate percentage. At 6% return: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years. At 10%: 72 ÷ 10 = 7.2 years. At 12%: 72 ÷ 12 = 6 years. This rule is most accurate for rates between 6-10%. For lower rates, use 69.3 instead of 72 for more precision. The Rule of 72 also works in reverse — if something doubles in 10 years, the growth rate is approximately 72 ÷ 10 = 7.2%.
How much should I save monthly for compound interest to reach my goal?
To calculate the monthly savings needed, work backwards from your goal. Use the formula: Monthly = Goal × (r/n) / ((1 + r/n)^(n×t) - 1), where r is annual rate, n is compounding frequency, and t is years. Examples at 7% return: For $100,000 in 10 years: ~$585/month. For $500,000 in 20 years: ~$956/month. For $1,000,000 in 30 years: ~$820/month. Notice how powerful time is — reaching $1M requires less monthly savings over 30 years than reaching $500K over 20 years. This is why starting early is the single most important factor in building wealth. Every year you delay roughly doubles the monthly amount needed.
What is a realistic interest rate to use for compound growth?
Historical averages provide guidance: The S&P 500 has returned approximately 10% annually since 1926 (about 7% after inflation). Bond funds have averaged 5-6%. High-yield savings accounts currently offer 4-5%. For long-term planning (20+ years), 7% (inflation-adjusted stock market return) is commonly used. For conservative estimates, use 5-6%. For aggressive estimates, use 8-10%. Never plan with returns above 10% unless you have a specific, proven strategy. Remember that actual returns vary widely year to year — the stock market can drop 30% in a bad year or gain 30% in a good year. The averages only work over long time horizons of 15+ years.
What is the difference between APR and APY when comparing accounts?
APR is the nominal annual rate before any intra-year compounding, while APY, also called the effective annual rate, is what a balance actually grows by over a full year once compounding is applied. Deposit institutions in the United States must quote APY under the Truth in Savings Act, and lenders quote APR under Truth in Lending. Comparing an APR against an APY is an apples-to-oranges error; convert everything to the effective rate before deciding.
How do you solve the compound interest formula for the rate or the number of years?
Both are recovered by rearranging the same equation. For the growth rate of a lump sum, take the ratio of ending to starting value, raise it to the power of one over the number of years, and subtract one; that is the compound annual growth rate. For time, divide the logarithm of the value ratio by the logarithm of one plus the periodic rate, then divide by periods per year. These inversions answer what return a goal requires, or how long it takes.
How do taxes on interest reduce the effective rate of compounding?
In a taxable account, interest and non-qualified distributions are taxed in the year they are credited, so the amount left to compound is the return multiplied by one minus your marginal rate. A 6 percent return taxed at 24 percent compounds at about 4.56 percent, and that drag itself compounds year after year. Tax-deferred and tax-free accounts avoid the annual haircut, which is the main reason the same investment builds more wealth inside a retirement wrapper.
When does investing a lump sum beat spreading the same money into monthly deposits?
Under a single positive assumed rate, the lump sum always wins, because every dollar starts compounding immediately rather than arriving over the following year. Splitting the money into instalments simply shortens the average time invested. The case for spreading deposits is behavioural and risk-based rather than mathematical: it removes the chance of committing everything just before a decline and matches how most people actually receive income, which the recurring contribution term models.
Why does a small change in the assumed rate produce such a large change over 30 years?
Because the rate sits in an exponent rather than a multiplier, its effect grows geometrically with the horizon. Depositing $500 a month for 30 years accumulates roughly $502,000 at 6 percent and about $610,000 at 7 percent, so one extra percentage point adds more than a fifth to the result. The same sensitivity works in reverse, which is why projections should be run across a range of rates rather than presented as a single confident number.
References
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