Frequency analysis summary
Balance growth chart
Equivalent rate conversion table
| Frequency | Periods per Year | Equivalent Periodic Rate |
|---|
Yearly schedule
| Year | Start Balance | Contributions | Interest | End Balance | Real End Value |
|---|
Enter calculator inputs
In physics, frequency measures repeating cycles. In finance, frequency controls compounding and payment timing. This tool compares both ideas through one practical value-growth model.
Example data table
| Initial Amount | Annual Rate | Years | Compounding | Contribution | Future Value | Real Future Value | Required Contribution |
|---|---|---|---|---|---|---|---|
| $10,000.00 | 8.00% | 5 | Monthly | $200.00 monthly | $29,593.83 | $26,156.63 | $273.58 monthly for $35,000 target |
Formula used
EAR = (1 + r / m)m - 1
EAR = er - 1
i = (1 + EAR)1 / p - 1
FVprincipal = P × (1 + i)n
FVannuity = PMT × [((1 + i)n - 1) / i]
For beginning contributions, multiply by (1 + i).
Real FV = FV / (1 + f)y
Here, r is the nominal annual rate, m is the compounding frequency, p is the contribution frequency, n is the total contribution periods, P is the initial amount, PMT is the recurring contribution, f is inflation, and y is years.
How to use this calculator
- Enter the starting amount and nominal annual rate.
- Select the compounding frequency used by the account or contract.
- Select how often you add or pay money.
- Enter an optional recurring contribution.
- Choose whether contributions happen at the beginning or end.
- Enter an optional inflation rate for real-value results.
- Enter a target future value to estimate the required recurring amount.
- Click Calculate to view metrics, schedule, conversions, and the Plotly chart.
- Use the CSV and PDF buttons to export your results.
FAQs
1) What does frequency mean here?
It means how often compounding or contributions occur each year. Higher frequency usually increases growth because interest is applied more often.
2) Why is there both compounding and contribution frequency?
Accounts may compound monthly while you contribute weekly. The calculator converts rates so both timelines work together consistently.
3) What is the effective annual rate?
It is the true yearly growth rate after compounding effects are included. It lets you compare different compounding schedules fairly.
4) What does real future value show?
It adjusts the ending value for inflation. This helps you estimate purchasing power rather than only the nominal balance.
5) When should I use beginning contributions?
Use beginning timing when deposits happen at the start of each period. This gives each deposit one extra period of growth.
6) What if I leave target future value empty?
The calculator still returns the full forecast. It simply skips the required contribution output for a target goal.
7) Can I use custom yearly frequencies?
Yes. Choose custom for compounding or contributions and enter your own periods per year for specialized schedules.
8) Why include a physics explanation?
Physics treats frequency as repeating cycles over time. Finance uses the same idea for repeating compounding and payment events.