Calculate simple and compound interest on loans and investments. Compare different interest types, rates, and time periods to understand the true cost or return on your money.
Interest is the cost of borrowing money or the return earned on investments. Understanding the difference between simple and compound interest is crucial for making informed financial decisions, whether you're saving for the future or taking out a loan.
Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal and accumulated interest. This fundamental difference can result in dramatically different outcomes over time.
I = Interest, P = Principal, r = Interest rate, t = Time
A = Final amount, n = Compounding frequency per year
The actual annual rate considering compounding frequency
| Principal: $10,000 at 6% | 5 Years | 10 Years | 20 Years | 30 Years |
|---|---|---|---|---|
| Simple Interest | $13,000 | $16,000 | $22,000 | $28,000 |
| Compound Interest (Annual) | $13,382 | $17,908 | $32,071 | $57,435 |
| Difference | $382 | $1,908 | $10,071 | $29,435 |
| Frequency | Formula Factor | $10,000 at 6% for 10 Years | Extra vs. Annual |
|---|---|---|---|
| Annual (n=1) | (1 + 0.06/1)^(1×10) | $17,908 | Base |
| Semi-annual (n=2) | (1 + 0.06/2)^(2×10) | $18,061 | +$153 |
| Quarterly (n=4) | (1 + 0.06/4)^(4×10) | $18,140 | +$232 |
| Monthly (n=12) | (1 + 0.06/12)^(12×10) | $18,194 | +$286 |
| Daily (n=365) | (1 + 0.06/365)^(365×10) | $18,220 | +$312 |
| Financial Product | Typical Rate Range | Interest Type | Compounding |
|---|---|---|---|
| Savings Account | 0.5% - 5% | Compound | Daily/Monthly |
| Certificate of Deposit | 2% - 6% | Compound | Various |
| Credit Cards | 15% - 25% | Compound | Daily |
| Personal Loans | 6% - 20% | Simple/Compound | Monthly |
| Mortgages | 3% - 8% | Compound | Monthly |
| Auto Loans | 3% - 12% | Simple | N/A |
Today's value of future money
Future value of today's money
Interest rate adjusted for inflation
Nominal Rate: The stated interest rate before considering compounding or inflation.
Effective Rate: The actual rate after accounting for compounding frequency.
APR (Annual Percentage Rate): Includes interest rate plus fees, standardized for comparison.
APY (Annual Percentage Yield): The effective annual rate of return including compounding.
| Time Period | Conversion to Years | Example Calculation |
|---|---|---|
| Days | Days ÷ 365 | 90 days = 90/365 = 0.247 years |
| Months | Months ÷ 12 | 18 months = 18/12 = 1.5 years |
| Quarters | Quarters ÷ 4 | 6 quarters = 6/4 = 1.5 years |
| Years | Already in years | 5 years = 5 years |
For Investments: Choose accounts with higher interest rates and more frequent compounding.
For Loans: Look for simple interest loans when possible, make extra principal payments.
Time Factor: Start saving early to maximize the benefit of compound interest.
Rate Shopping: Small differences in rates can lead to significant differences over time.
Confusing Nominal and Effective Rates: Always compare effective rates (APY) for fair comparison.
Ignoring Compounding: Not accounting for how often interest compounds can lead to wrong estimates.
Wrong Time Units: Make sure rate and time periods match (annual rate with years).
Forgetting Fees: Interest rate isn't the only cost - consider all fees and charges.