What is Compound Interest?
Compound interest is the interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which is calculated only on the principal), compound interest grows exponentially over time — earning "interest on interest." This is the fundamental principle behind long-term wealth building.
Compound Interest Formula
The compound interest formula is:
A = P × (1 + r/n)n×t
- A — final amount (principal + interest)
- P — initial principal balance
- r — annual interest rate (as a decimal, e.g. 8% = 0.08)
- n — number of times interest is compounded per year
- t — time in years
Simple vs. Compound Interest
Simple interest is calculated only on the original principal. For example, $1,000 at 8% simple interest for 10 years earns $800 in interest (final balance: $1,800).
Compound interest (monthly, 8% rate) on the same $1,000 over 10 years yields a final balance of $2,219.64 — earning $419.64 more than simple interest. The difference grows dramatically over longer periods.
Compounding Frequency
Compounding frequency is how often interest is calculated and added to the principal each year. More frequent compounding results in a higher final balance:
- Annually (1/yr) — interest added once per year
- Semi-annually (2/yr) — interest added every 6 months
- Quarterly (4/yr) — interest added every 3 months
- Monthly (12/yr) — interest added every month (most common for savings accounts)
- Weekly (52/yr) — interest added every week
- Daily (365/yr) — interest added every day
Compound Interest Examples
Example 1 — Basic calculation of the value of an investment
You invest $1,000 at an annual interest rate of 8%, compounded monthly for 20 years. What is the final balance?
A = 1000 × (1 + 0.08/12)12×20 = 1000 × (1.00667)240 ≈ $4,926.80
Total compound interest earned: $3,926.80
Example 2 — Complex calculation with additional monthly deposits
Start with $5,000, add $200/month, at 7% annual rate compounded monthly for 30 years:
- Future value of principal: $5,000 × (1 + 0.07/12)360 ≈ $38,061
- Future value of monthly deposits: $200 × [((1.00583)360 − 1) / 0.00583] ≈ $227,977
- Total final balance: ≈ $266,038
- Total deposited: $5,000 + $72,000 = $77,000
- Total interest earned: ≈ $189,038
Example 3 — Calculating the interest rate of an investment
If you invest $10,000 and want it to grow to $25,000 in 15 years with annual compounding, what interest rate do you need?
25,000 = 10,000 × (1 + r)15 → r = (2.5)1/15 − 1 ≈ 6.30% per year
Example 4 — Calculating the doubling time of an investment
The Rule of 72 provides a quick estimate: divide 72 by the annual interest rate to find how many years it takes for your investment to double.
- At 6% → doubles in 72 / 6 = 12 years
- At 8% → doubles in 72 / 8 = 9 years
- At 12% → doubles in 72 / 12 = 6 years
Compound Interest Table
Final balance of $1,000 invested at various rates over time (monthly compounding):
| Rate / Years | 5 yrs | 10 yrs | 20 yrs | 30 yrs |
|---|---|---|---|---|
| 3% | $1,161 | $1,349 | $1,820 | $2,454 |
| 5% | $1,284 | $1,647 | $2,712 | $4,467 |
| 7% | $1,418 | $2,009 | $4,038 | $8,116 |
| 10% | $1,645 | $2,707 | $7,328 | $19,837 |
| 12% | $1,817 | $3,300 | $10,893 | $35,950 |
How to Use the Compound Interest Calculator
- Enter initial balance — the amount you have invested or saved.
- Select currency — choose from 26 world currencies including USD, EUR, GBP, JPY, and more.
- Input interest rate — the annual interest rate your investment will earn.
- Set the term — number of years and months for the investment to grow.
- Select compounding frequency — annually, semi-annually, quarterly, monthly, weekly, or daily.
- Additional deposits (optional) — specify recurring deposit amount, frequency, and whether deposits are made at the beginning or end of the period.
- Review results — see final balance, total interest, and year-by-year growth.
Behind the Scenes
For additional periodic deposits, the calculator uses the future value of an annuity formula, converting your deposit frequency to align with the compounding frequency:
FVdeposits = PMT × [((1 + eff)m − 1) / eff]
Where eff is the effective rate per deposit period and m is the total number of deposit periods. If deposits are made at the beginning of each period (annuity due), the result is multiplied by (1 + eff).
Frequently Asked Questions
What is the best compounding frequency?
Daily compounding yields the highest return, but the difference between daily and monthly compounding is minimal for most practical purposes. Monthly compounding is the most common for savings accounts and CDs.
How much does compound interest grow over time?
The power of compound interest becomes most visible over long time horizons. $10,000 at 7% annual interest grows to $76,123 in 30 years — more than 7x the original investment — with no additional deposits.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal annual rate. APY (Annual Percentage Yield) accounts for compounding and reflects the actual return earned in a year. Higher compounding frequency means APY > APR.
Can I use this calculator for different currencies?
Yes! The calculator supports 26 world currencies including USD, EUR, GBP, JPY, CHF, CAD, AUD, CNY, INR, BRL, and many more. The currency selection affects only the display symbol — the math is identical across all currencies.