Compound Interest Calculator
Calculate compound interest with regular monthly contributions. See how your money grows over time with the power of compounding. See also Simple Interest Calculator and Loan Calculator.
How Compound Interest Works
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only earns on the principal), compound interest creates a snowball effect where your money grows exponentially over time. Albert Einstein reportedly called it the "eighth wonder of the world." The more frequently interest compounds, the faster your money grows.
Compound Interest Formula
A = P × (1 + r/n)^(n×t)
Where:
A = Future value
P = Principal (initial investment)
r = Annual interest rate (decimal)
n = Compounding frequency per year
t = Time in years
Example
$10,000 at 7% for 10 years, compounded monthly
A = 10000 × (1 + 0.07/12)^(12×10)
A = 10000 × (1.005833)^120
A = $20,096.61
Interest earned: $10,096.61
The Power of Regular Contributions
Adding regular monthly contributions dramatically accelerates wealth building. For example, $10,000 invested at 7% for 10 years grows to about $20,097. But adding just $200/month turns that into approximately $54,800. The monthly contributions add $24,000 in principal, but compound interest adds an extra $20,800 on top. Starting early and contributing consistently is the most powerful wealth-building strategy available to most people.
Compound Interest Growth Table
| Initial | Monthly | Rate | 10 Years | 20 Years | 30 Years |
|---|---|---|---|---|---|
| $1,000 | $100 | 7% | $18,417 | $53,998 | $122,709 |
| $5,000 | $200 | 7% | $39,835 | $110,996 | $250,418 |
| $10,000 | $500 | 7% | $106,588 | $271,490 | $604,046 |
| $10,000 | $0 | 10% | $25,937 | $67,275 | $174,494 |
| $0 | $500 | 7% | $86,541 | $260,464 | $584,893 |
Frequently Asked Questions
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously accumulated interest. Over time, compound interest grows much faster because you earn "interest on interest."
How often should interest compound?
More frequent compounding produces slightly higher returns. Daily compounding earns more than monthly, which earns more than annually. However, the difference between daily and monthly compounding is small. Most savings accounts compound daily, while most investments compound monthly or quarterly.
What is the Rule of 72?
The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by the annual interest rate. At 7%, your money doubles in approximately 72/7 = 10.3 years. At 10%, it doubles in about 7.2 years.
Solved Examples
Example 1: Long-term retirement savings with monthly contributions
Solution:
Principal (P) = $10,000, Monthly contribution = $500, Rate = 7%, Time = 30 years, Compounding = Monthly
Step 1: Each month, add $500 and apply monthly rate of 7%/12 = 0.5833%
Step 2: After 30 years of compounding with contributions:
Total contributions = $10,000 + ($500 × 360) = $190,000
Future Value ≈ $604,046
Total interest earned ≈ $414,046
Answer: $604,046 (more than 3× your contributions due to compounding)
Example 2: Comparing 10-year vs 20-year investment horizon
Solution:
Principal = $25,000, Rate = 8%, Monthly contribution = $300, Compounding = Monthly
After 10 years: FV ≈ $108,826 (Contributions: $61,000, Interest: $47,826)
After 20 years: FV ≈ $310,868 (Contributions: $97,000, Interest: $213,868)
The extra 10 years adds $202,042 — mostly from interest on interest
Answer: Doubling your time nearly triples your money. $310,868 vs $108,826.
Example 3: Effect of compounding frequency on $50,000
Solution:
Principal = $50,000, Rate = 6%, Time = 15 years, No additional contributions
Annually: $50,000 × (1 + 0.06)^15 = $119,828
Quarterly: $50,000 × (1 + 0.015)^60 = $121,989
Monthly: $50,000 × (1 + 0.005)^180 = $122,709
Daily: $50,000 × (1 + 0.06/365)^5475 = $122,891
Answer: Daily compounding yields $3,063 more than annual compounding over 15 years.
Example 4: Starting early — age 25 vs age 35
Solution:
Both invest $200/month at 7% until age 65, compounded monthly
Starting at 25 (40 years): FV ≈ $528,025 (Contributed: $96,000)
Starting at 35 (30 years): FV ≈ $243,994 (Contributed: $72,000)
Extra 10 years of compounding = $284,031 more, despite only $24,000 extra in contributions
Answer: Starting 10 years earlier more than doubles your final wealth ($528,025 vs $243,994).
Practice Questions
Try these on your own:
- You invest $5,000 at 6% compounded monthly for 10 years with no additional contributions. What is the future value? (Answer: $9,096.98)
- If you contribute $1,000/month at 8% annual rate compounded monthly for 20 years starting with $0, how much will you have? (Answer: $592,947)
- A $20,000 investment grows to $80,000 in 15 years. What was the annual compound growth rate? (Answer: ≈9.68%)
- How long does it take $10,000 to double at 5% compounded annually? Use the Rule of 72. (Answer: ≈14.4 years)
- Compare: $100,000 at 7% for 25 years compounded annually vs quarterly. What is the difference? (Answer: Annually = $542,743; Quarterly = $557,234; Difference = $14,491)
- You want $1,000,000 in 30 years. At 7% compounded monthly, how much must you invest per month starting from $0? (Answer: ≈$820/month)
Common Mistakes to Avoid
One of the most common errors is confusing the compounding frequency with the contribution frequency. If your interest compounds monthly but you contribute quarterly, the calculation differs significantly. Another frequent mistake is using the annual rate directly in the formula without dividing by the number of compounding periods — you must use r/n, not r. Many people also forget that inflation erodes purchasing power, so a 7% nominal return with 3% inflation yields only about 4% real growth. Additionally, investors often underestimate the impact of fees: a 1% annual management fee on a portfolio earning 7% effectively reduces your compounding rate to 6%, which over 30 years can cost you hundreds of thousands of dollars. Finally, be careful not to confuse APR (annual percentage rate) with APY (annual percentage yield) — APY accounts for compounding and is always slightly higher than APR for the same nominal rate.
Key Takeaways
- Compound interest earns "interest on interest," creating exponential growth over time.
- Starting early matters more than investing more — 10 extra years can double your final amount.
- More frequent compounding (daily vs annually) yields modestly higher returns, typically 1-3% more over long periods.
- Regular monthly contributions dramatically amplify the compounding effect compared to a single lump sum.
- The Rule of 72 provides a quick estimate: divide 72 by the interest rate to find doubling time.
- Always account for inflation, fees, and taxes when projecting real investment growth.