Periodic Interest Rate Calculator
Convert between nominal, effective, and periodic interest rates with different compounding frequencies
How to Use Periodic Interest Rate Calculator
Interest Rate Conversion
This calculator helps you convert interest rates between different compounding periods and calculate the effective annual yield.
Step-by-Step Guide:
- Enter the nominal (annual) interest rate
- Select the current compounding frequency
- Choose the desired compounding frequency
- Click "Calculate" to see results
Key terms:
- Nominal Rate: The stated annual interest rate without accounting for compounding
- Effective Annual Rate (APY): The actual annual rate accounting for compounding
- Periodic Rate: The rate applied for each compounding period
Future Value Projection
Calculate how an investment will grow over time with compound interest.
How to use:
- Enter your initial investment amount
- Specify the annual interest rate
- Select the compounding frequency
- Enter the investment time period in years
- Click "Calculate" to view the results and growth chart
Formulas Used
Converting between different compounding periods:
To convert from one periodic rate to another:
Where n is the number of compounding periods per year
Calculating future value:
Where:
- P = Principal (initial investment)
- r = Annual nominal interest rate (decimal)
- n = Number of compounding periods per year
- t = Time in years
For continuous compounding:
Where e is the mathematical constant approximately equal to 2.718281828459
Practical Examples
Example 1: Mortgage Rate Conversion
A bank offers a mortgage with a 6% annual rate, compounded monthly. What is the effective annual rate?
- Enter 6.00 as the Nominal Rate
- Select "Monthly" as From Compounding
- Select "Annually" as To Compounding
- Result: Effective Annual Rate (APY) = 6.17%
Example 2: Investment Growth
If you invest $10,000 at 5% annual interest, compounded quarterly for 10 years, how much will you have?
- Initial investment: $10,000
- Annual interest rate: 5%
- Compounding: Quarterly
- Time period: 10 years
- Result: Future Value = $16,386.16
Example 3: Daily vs. Monthly Compounding
Compare the difference between daily and monthly compounding for a 3% annual rate on $5,000 over 5 years.
- Monthly compounding: $5,000 grows to $5,805.43
- Daily compounding: $5,000 grows to $5,811.57
- Difference: $6.14 more with daily compounding
Compounding Frequency Comparison
This table demonstrates how different compounding frequencies affect the growth of an investment (based on a $10,000 principal and 5% annual interest rate).
| Compounding Frequency | Effective Annual Rate (APY) | Periodic Rate | Value after 1 Year | Value after 5 Years | Value after 10 Years |
|---|---|---|---|---|---|
| Annually (1/year) | 5.000% | 5.000% per year | $10,500.00 | $12,762.82 | $16,288.95 |
| Semi-annually (2/year) | 5.063% | 2.500% per period | $10,506.25 | $12,833.59 | $16,453.09 |
| Quarterly (4/year) | 5.095% | 1.250% per quarter | $10,509.45 | $12,869.56 | $16,536.89 |
| Monthly (12/year) | 5.116% | 0.417% per month | $10,511.62 | $12,889.93 | $16,582.91 |
| Daily (365/year) | 5.127% | 0.014% per day | $10,512.67 | $12,899.46 | $16,604.71 |
| Continuously | 5.127% | N/A | $10,512.71 | $12,899.68 | $16,605.21 |
Understanding Interest Rates
Types of Interest Rates
- Nominal Rate: The stated annual interest rate without considering compounding
- Effective Annual Rate (EAR/APY): The actual annual yield when accounting for compounding
- Periodic Rate: The rate applied during each compounding period
- Real Interest Rate: The interest rate adjusted for inflation
Compounding Effects
More frequent compounding leads to higher effective returns:
- Interest earned in earlier periods itself earns interest
- The difference becomes more significant with higher interest rates
- The difference becomes more pronounced over longer time periods
- Continuous compounding represents the mathematical limit of compounding frequency
Common Applications
Loans and Mortgages
Most loans use monthly compounding. Converting between APR and APY helps understand the true cost of borrowing.
Savings Accounts
Banks may advertise the APY to show the effective return but calculate interest using daily or monthly compounding.
Investment Planning
Understanding compounding helps make accurate projections for retirement and long-term investment goals.
Financial Comparisons
Converting all rates to the same basis (like APY) allows for fair comparison between different investment options.