Compound Interest Calculator
Calculate compound interest growth for investments, savings, and loans. See how compounding frequency (daily, monthly, annually) affects your returns.
💰 Finance📐 A = P(1 + r/n)^(nt) + PMT[((1+r/n)^(nt)-1)/(r/n)]
Principal ($)
Annual interest rate (%)
Years
Monthly contribution ($)
Compounding frequency
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Compound Interest Calculator | A = P(1 + r/n)^(nt) + PMT[((1+r/n)^(nt)-1)/(r/n)] | $ final |
Step-by-Step Examples
Example 1
Retirement Savings
$5K start, 7%, 20 years, $200/month, monthly.
- Principal growth: $5K x 1.0058^240 = $19,890
- PMT growth: $200 x ((1.0058^240-1)/0.0058) = $129,978
- Total: $149,868 | Contributed: $53,000
- Interest earned: $96,868
✓ $149,868 total
Example 2
Pure Compound
$10K, 8%, 30 years, no contributions.
- $10K x (1+0.0067)^360 = $109,357
- 10x growth in 30 years at 8%
✓ $109,357
Example 3
High Contributions
$0 start, 7%, 10 years, $500/month.
- PMT: $500 x ((1.0058^120-1)/0.0058) = $86,930
- Contributed: $60,000 | Earned: $26,930
✓ $86,930
Real-World Applications
Investors
Visualize long-term investment growth with compound interest.
Financial Education
Teach the power of compound interest and early investing.
Financial Planners
Model retirement savings scenarios for clients.
Savers
Compare high-yield savings account growth over different periods.
Common Mistakes to Avoid
⚠️
Underestimating the early start advantage
Starting 10 years earlier with the same total contributions can result in 2-4x more wealth at retirement. The early years of compounding are most valuable.
⚠️
Ignoring inflation
7% nominal return at 3% inflation = ~4% real return. Inflation erodes purchasing power; factor it into long-term projections.
⚠️
Confusing interest rate with return
Stock market average returns (~10% nominal, ~7% real) are not guaranteed. Bank savings accounts (4-5% APY) are guaranteed but much lower. Use conservative rates for planning.
Frequently Asked Questions
What is compound interest? ▾
Interest earned not only on the principal but also on previously earned interest. $1,000 at 7% for 30 years compounding monthly grows to $8,116 - 8x more than simple interest of $1,000 + $2,100 = $3,100.
Rule of 72 for doubling time? ▾
Divide 72 by the interest rate to estimate years to double. At 7%: 72/7 = 10.3 years. At 10%: 72/10 = 7.2 years. At 4%: 72/4 = 18 years.
Daily vs monthly vs annual compounding? ▾
More frequent compounding = slightly more growth. $10,000 at 7% for 20 years: annual = $38,697; monthly = $40,064; daily = $40,138. Difference is small; rate matters much more than compounding frequency.
What is the S&P 500 average return? ▾
Approximately 10% annually nominal (including dividends) over the long term, or about 7% after inflation. Individual years vary greatly; long-term investors should expect years of -20% to -40% declines before recovery.
When does compound interest work against you? ▾
On credit card debt (22-29% APR) and payday loans. A $1,000 credit card balance at 22% compounds into $3,212 in 5 years if minimum payments are made. Compound interest works powerfully for AND against you.