Compound Savings Calculator
See how saving a small daily amount grows over time with compound interest.
Calculate the future value of saving $X per day.
Compound interest savings growth is the mechanism by which interest earns interest — causing savings to grow exponentially rather than linearly. Albert Einstein allegedly called compound interest “the eighth wonder of the world,” and while the attribution is disputed, the math is undeniable.
Compound interest formula: A = P × (1 + r/n)^(n×t)
Where:
- A = final amount (principal + interest)
- P = principal (initial deposit)
- r = annual interest rate (decimal form: 5% = 0.05)
- n = compounding frequency per year (1=annual, 4=quarterly, 12=monthly, 365=daily)
- t = time in years
Future value with regular contributions: A = P × (1 + r/n)^(n×t) + PMT × ((1 + r/n)^(n×t) − 1) / (r/n)
Where PMT = regular deposit per compounding period.
Rule of 72 (quick doubling estimate): Years to Double = 72 / Annual Interest Rate (%) At 6%: 72/6 = 12 years to double. At 9%: 72/9 = 8 years.
Compounding frequency impact (on $10,000 at 5% for 10 years):
| Compounding | Final Value |
|---|---|
| Annual (n=1) | $16,288.95 |
| Quarterly (n=4) | $16,436.19 |
| Monthly (n=12) | $16,470.09 |
| Daily (n=365) | $16,486.65 |
Monthly vs. annual difference: only $181 over 10 years — compounding frequency matters far less than rate and time.
Worked example: $5,000 initial deposit + $300/month contribution at 6% annual rate, compounded monthly, for 20 years: P = $5,000, PMT = $300, r = 0.06, n = 12, t = 20 A = $5,000 × (1.005)^240 + $300 × ((1.005)^240 − 1) / 0.005 = $5,000 × 3.310 + $300 × 462.04 = $16,551 + $138,613 = $155,164
Total deposited: $5,000 + $300 × 240 = $77,000. Interest earned: $78,164 — more than the principal invested.