Example reference table
| APY (%) | Monthly rate (%) | Compounding |
|---|
Summary
Balance chart
Sensitivity snapshot
| APY scenario | APY (%) | Ending balance |
|---|
Monthly schedule
| # | Date | Start balance | Interest | Contribution | Fee | End balance | Real end |
|---|
Formula used
APY ↔ Periodic rate
For compounding frequency m per year, APY relates to nominal periodic rate
i_p by (1 + i_p/m)^m - 1 = APY.
Hence i_p = m\*\big((1+APY)^{1/m}-1\big).
Effective monthly rate from compounding
Using i_p, an effective monthly rate is
r_m = (1 + i_p/m)^{m/12} - 1.
With contributions at start, apply contributions before interest accrual.
Cash flow with taxes, fees, growth
Monthly interest I_t = B_{t-1}\*r_m, tax T_t = I_t\*τ.
Contribution grows monthly by g_m.
End balance:
B_t = (B_{t-1} + C_t^{eff})\*(1+r_m) - T_t - F_t for end-timing,
or apply C_t^{eff} pre-interest for start-timing.
How to use
- Choose mode and compounding frequency.
- Enter APY or monthly rate, timeframe, and balances.
- Optionally add teaser rate months, taxes, inflation, and fees.
- Add contribution growth and any lump-sum months.
- Click Calculate for table, chart, summary, and sensitivity.
- Optionally set a target and press Solve Contribution.
- Export to CSV or print-ready PDF when satisfied.
Rates are entered as percentages; e.g., 5% as 5.
Reference data & insights
1) APY, APR, and effective monthly rate
| Term | Meaning | Example value |
|---|---|---|
| APY | Yield including compounding. | 5.0000% |
| APR | Simple annual rate, no compounding. | 4.8891% |
| Monthly rate | Effective monthly growth from APY. | 0.4074% |
2) APY ↔ monthly rate conversion examples
| APY (%) | Monthly rate (%) | Factor (1+r)12 |
|---|---|---|
| 2.00 | 0.1650 | 1.0200 |
| 5.00 | 0.4074 | 1.0500 |
| 8.00 | 0.6434 | 1.0800 |
3) Compounding frequency effect on monthly rate
| APY fixed at 5% | m (per year) | Effective monthly rate (%) |
|---|---|---|
| Daily compounding | 365 | 0.4059 |
| Monthly compounding | 12 | 0.4074 |
| Quarterly compounding | 4 | 0.4092 |
| Annual compounding | 1 | 0.4074 |
4) Contribution timing impact (start vs end)
| Setting | Monthly rate 0.4074% | Contribution | Months | Ending balance |
|---|---|---|---|---|
| Start-of-month | 0.4074% | $200 | 24 | Higher |
| End-of-month | 0.4074% | $200 | 24 | Lower |
5) Taxes and inflation illustration
| Scenario | Tax on interest | Inflation | Real ending vs nominal |
|---|---|---|---|
| No frictions | 0% | 0% | Real equals nominal |
| With taxes | 30% | 0% | Lower nominal and real |
| With inflation | 0% | 3% | Nominal same; real lower |
| Taxes + inflation | 30% | 3% | Both effects combined |
Mini Glossary
- APY
- Annual percentage yield. Includes compounding within the year. Best for deposit growth comparisons.
- APR
- Annual percentage rate. Simple yearly rate without compounding. Often used for loans and credit.
- EAR
- Effective annual rate. Actual yearly growth from a periodic rate with compounding. Equivalent concept to APY in savings contexts.
- Nominal rate
- Quoted rate that does not specify or embed compounding. Requires compounding frequency to determine effective growth.
- Effective rate
- Rate that reflects compounding for the stated period. Example: effective monthly rate or effective annual rate.
- Nominal vs effective
- Nominal states the rate; effective shows realized growth after compounding. Convert using the compounding frequency to compare products fairly.
Frequently Asked Questions
1) What is APY?
APY is annual percentage yield. It includes compounding within the year, showing true growth from interest-on-interest. It is ideal for comparing savings and deposits paying periodic interest at different compounding frequencies.
2) How do I convert APY to a monthly rate?
Use the relationship: monthly rate equals (1 + APY)1/12 − 1. Enter APY and the calculator derives a consistent monthly rate for projections and schedules with your selected compounding frequency.
3) Why do start-of-month contributions end higher?
Contributions made at the start of each month get one extra month of compounding compared with end-of-month contributions. Earlier cash earns interest longer, therefore the final balance is higher under identical rates, fees, and timeframes.
4) Do fees reduce APY?
Fees don’t change the stated APY, but they reduce your realized return. The calculator subtracts monthly fees from the balance, so less money compounds, lowering total interest and the ending balance versus a no-fee scenario.
5) How are taxes handled here?
The tool applies your chosen tax rate to each month’s gross interest, then compounds the net interest. Real-world taxation varies by jurisdiction and account type. Confirm your situation with official guidance or a qualified professional.
6) What does “real balance” mean?
Real balance adjusts nominal results for inflation using your annual inflation input. It estimates purchasing power by deflating nominal balances monthly, providing a clearer picture of what future balances may buy in today’s terms.
7) Can APY be negative?
Yes, in rare cases with negative rates or certain fees overwhelming interest. The calculator supports negative APY inputs, projecting balances accordingly. Verify values and assumptions before relying on projections for financial decisions.