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 × ((1.005833)^480 - 1) / 0.005833 = $791,957 Total contributed: $300 × 480 = $144,000 Interest: $647,957 Person B (30 years): FV = $300 × ((1.005833)^360 - 1) / 0.005833 = $365,991 Total contributed: $300 × 360 = $108,000 Interest: $257,991
Result:10 years earlier = $425,966 MORE (2.16x) 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 simple and compound interest?
Simple interest is calculated only on the original principal (SI = P × r × t). Compound interest applies to the growing balance — each period's earned interest is added to principal before the next calculation (A = P(1 + r/n)^nt). On $10,000 at 8% over 20 years, simple interest yields $26,000 while annual compounding yields $46,610 — a 79% difference. High-yield accounts advertise APY to reflect compounding rather than the lower nominal rate.
References
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