Calculator Inputs
Example Data Table
This sample uses $500.00 monthly payments, 6.00% annual rate, 5.00 years, an ordinary annuity, and $1,000.00 as starting balance.
Example Contributions: $31,000.00
Example Interest: $5,233.87
| Period | Starting Balance | Payment | Interest | Ending Balance |
|---|---|---|---|---|
| 1 | $1,000.00 | $500.00 | $5.00 | $1,505.00 |
| 2 | $1,505.00 | $500.00 | $7.52 | $2,012.53 |
| 3 | $2,012.53 | $500.00 | $10.06 | $2,522.59 |
| 4 | $2,522.59 | $500.00 | $12.61 | $3,035.20 |
| 5 | $3,035.20 | $500.00 | $15.18 | $3,550.38 |
| 6 | $3,550.38 | $500.00 | $17.75 | $4,068.13 |
| Final Future Value | $36,233.87 | |||
Formula Used
This calculator uses an equivalent periodic rate so it can handle different payment and compounding frequencies accurately. First, it converts the nominal annual rate into an effective annual rate:
EAR = (1 + r / m)m - 1
It then converts that annual rate into the payment period rate:
i = (1 + EAR)1 / p - 1
Here, r is the annual nominal rate, m is compounding periods per year,
and p is payment periods per year.
For an ordinary annuity, each period follows:
Ending Balance = Starting Balance × (1 + i) + Payment
For an annuity due, each period follows:
Ending Balance = (Starting Balance + Payment) × (1 + i)
If payments grow each year, the calculator converts the annual payment growth into a matching payment period growth and updates every contribution before compounding.
When payment and compounding frequencies match, the traditional closed forms are also consistent with the results:
FV ordinary = P × [((1 + i)n - 1) / i]
FV due = FV ordinary × (1 + i)
How to Use This Calculator
- Enter the amount deposited every payment period.
- Enter the annual nominal interest rate.
- Set the saving horizon in years.
- Choose the payment frequency and compounding frequency.
- Pick ordinary annuity for end-of-period payments or due for beginning-of-period payments.
- Add any starting balance to include a lump sum already invested.
- Use annual payment growth if contributions increase over time.
- Choose your preferred currency symbol and rounding decimals.
- Click the calculate button to show future value, schedule, and graph.
- Use the CSV and PDF buttons to export your results.
Frequently Asked Questions
1. What is a future value annuity?
It is the value of repeated deposits grown to a chosen future date. The calculator adds each payment and compounds it according to your selected timing and rate settings.
2. What is the difference between ordinary annuity and annuity due?
An ordinary annuity assumes payments are made at the end of each period. An annuity due assumes payments are made at the beginning, giving each payment one extra period of growth.
3. Why can payment frequency differ from compounding frequency?
Many savings plans accept deposits monthly while interest compounds daily or quarterly. This calculator converts rates properly so the final balance reflects that mismatch more accurately.
4. What does annual payment growth mean?
It lets contributions increase over time. For example, you may raise monthly deposits each year after a salary increase. The calculator converts that annual growth into each payment period automatically.
5. Does the starting balance affect every result?
Yes. The starting balance is treated like money already invested at time zero, so it compounds over the full saving horizon and increases the final future value.
6. What happens if the interest rate is zero?
The future value becomes the sum of the starting balance and all contributions, adjusted only for any payment growth. No interest is added to the schedule.
7. Why does the schedule matter?
The schedule shows each period’s starting balance, payment, interest, and ending balance. It helps verify assumptions, compare scenarios, and export a detailed record for planning.
8. Can I use this for retirement or education planning?
Yes. It is useful for any recurring savings goal, including retirement, tuition, emergency funds, down payments, and sinking funds where regular deposits matter.