Where does the projected balance come from?
This breakdown keeps your own money separate from modelled interest, so the effect of the rate and time assumption remains visible.
Change any input above and the interpretation updates automatically.
Rate sensitivity: how much does one percentage point change the result?
The table recalculates the same starting amount, contribution schedule and term at a rate one percentage point lower and one percentage point higher than your input. It is a sensitivity test, not a forecast.
| Scenario | Annual rate input | Final balance | Interest earned |
|---|---|---|---|
| — | |||
Contribution timing check – beginning vs end of the period
Two saving plans can use the same contribution amount and frequency but produce slightly different balances if one contribution reaches the account earlier. This is especially noticeable over long terms.
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Year-by-year growth from your inputs
The table tracks cumulative money contributed and estimated interest at each full year, plus the final partial year when extra months are entered. For a quick manual lookup without custom inputs, use the Compound Interest Factor Table.
| Time | Total contributed | Interest earned | Balance |
|---|---|---|---|
| — | |||
How compound interest is calculated
For a lump sum with a nominal annual rate, the basic model divides the annual rate by the number of compounding periods and applies that periodic rate repeatedly. The effect becomes stronger when interest remains in the balance and can itself earn interest later.
When you select effective annual rate (APY/AER), the annual compounding effect is already included in the rate. In that mode, the calculator treats the entered percentage as the total one-year growth rate rather than applying another compounding-frequency adjustment.
Regular contributions are added on a monthly planning timeline according to the selected frequency and timing. Each contribution then grows for the time remaining in the term. This makes the contribution timing visible without pretending that every bank or investment platform uses the same posting convention.
Nominal annual rate
A nominal annual rate is a stated annual percentage before the effect of within-year compounding. If 5% is compounded monthly, the calculator applies twelve periodic compounding intervals and the effective annual rate is slightly above 5%.
Use this mode only when the rate you have is genuinely nominal and the compounding frequency is known or intentionally assumed.
Effective annual rate (APY/AER)
An effective annual rate represents the total growth over one year after compounding. APY and AER are common labels for this idea in different markets and products.
If your provider gives an APY/AER, select the effective-rate mode. Otherwise you could accidentally add a second compounding effect that is not part of the quoted rate.
Where can you get the input data?
| Input | Where to find it | What to check |
|---|---|---|
| Starting amount | Your current balance or the lump sum you plan to deposit. | Use the amount that is actually available to grow; do not include money you do not intend to place in this scenario. |
| Annual rate | Account disclosure, product information or a clearly stated planning assumption. | Identify whether it is nominal or an effective annual rate such as APY/AER. Do not treat an uncertain future investment return as guaranteed. |
| Compounding frequency | Product terms or account documentation. | This matters in nominal-rate mode. In APY/AER mode, the annual compounding effect is already included. |
| Regular contribution | Your savings plan, standing order or budget. | Use an amount and schedule you actually intend to model. Zero is valid for a lump-sum-only scenario. |
| Term | Your planning horizon. | Separate the mathematical projection from any product maturity, withdrawal restriction or tax rule. |
Worked example: $10,000 plus $200 per month
Suppose you start with $10,000, add $200 at the end of every month and model a nominal 5% annual rate compounded monthly for 10 years. The starting amount grows for the whole term, while each later contribution has less time to compound.
With these assumptions, the calculator projects a final balance of roughly $47,500. Your own money contributed is $34,000: the $10,000 starting amount plus $24,000 of monthly deposits. The remaining roughly $13,500 is modelled interest.
The important lesson is not the exact dollar amount. It is the separation between money you add and growth generated by the assumed rate. If the rate, contribution timing or contribution amount changes, the result changes too.
Does your result look realistic?
Check the rate type first. A common error is entering an APY/AER as though it were a nominal annual rate and then selecting monthly or daily compounding, which can overstate the intended growth. Also confirm that the contribution frequency matches the amount: $200 monthly is very different from $200 annually. Finally, remember that a constant rate is a mathematical assumption, not a promise that a real account or investment will deliver the same return every year.
Practice problems – solve them before revealing the answer
Use these as short self-check exercises. Work out the result with the formulas from this page first, then use Show answer to compare your method and result. These buttons do not change the calculator inputs.
Exercise 1 – monthly saver
You start with $1,000, add $100 at the end of every month, and use a 4% nominal annual rate compounded monthly for 5 years.
Find: the effective annual rate, total contributed, final balance and interest earned.
Monthly rate = 4% ÷ 12 = 0.3333%. Effective annual rate ≈ 4.074%.
Total contributed = $1,000 + (60 × $100) = $7,000.00.
Projected final balance ≈ $7,850.89.
Modelled interest ≈ $7,850.89 − $7,000.00 = $850.89.
Exercise 2 – effective annual rate
You start with $10,000, add $300 at the end of every month, and use a 6% effective annual rate (APY/AER) for 20 years.
Find: total contributed, final balance, interest earned and explain why no extra compounding-frequency adjustment is applied.
The 6% rate is already an effective annual rate, so its one-year compounding effect is already included. It must not be compounded again as though it were a nominal rate.
Total contributed = $10,000 + (240 × $300) = $82,000.00.
Projected final balance ≈ $168,102.94.
Modelled interest ≈ $86,102.94, about 51.2% of the final balance.
Exercise 3 – lump sum only
You invest €20,000 with no regular contributions at a 5% nominal annual rate compounded quarterly for 10 years.
Find: the quarterly rate, number of compounding periods, effective annual rate, final balance and interest earned.
Quarterly rate = 5% ÷ 4 = 1.25%. Number of periods = 4 × 10 = 40.
Effective annual rate = (1 + 0.05 ÷ 4)4 − 1 ≈ 5.095%.
Final balance = €20,000 × (1.0125)40 ≈ €32,872.39.
Interest earned ≈ €12,872.39.
What changes the final balance the most?
Time determines how long previous interest can remain in the balance and compound. The assumed rate changes the growth factor applied over that time. Contributions add new principal, and earlier contributions generally have more time to grow than later ones.
These drivers interact. A small rate difference can become important over a long horizon, but increasing the amount you actually contribute can also dominate the result. The rate-sensitivity table above helps separate those effects instead of relying on one headline projection.
For personal planning, it is usually more useful to compare several reasonable scenarios than to make a decision from one optimistic assumption.
Common compound-interest calculation mistakes
- Confusing a nominal annual rate with APY/AER and applying compounding twice.
- Entering a monthly contribution while leaving the frequency set to annually, or the reverse.
- Assuming contributions made at the beginning and end of a period have identical growth time.
- Treating a constant assumed investment return as a guaranteed future return.
- Ignoring fees, taxes or inflation when those factors matter to the real decision.
- Comparing two scenarios that use different contribution amounts or terms without noticing the changed assumption.
- Rounding each month manually instead of keeping full precision until the displayed result.
For finance and business students: how to calculate compound growth with regular contributions
A compound-interest problem with regular saving contains two different future-value calculations. The starting principal is present from day one and can grow for the whole term. Regular contributions arrive later, so each deposit has less time to earn interest. Keeping these two parts separate is the easiest way to understand the mathematics and to avoid treating interest as though it were money you personally contributed.
1. Identify the variables before using a formula
For a monthly example, let P be the starting principal, PMT the regular monthly contribution, r the nominal annual rate written as a decimal, i the periodic monthly rate and n the number of monthly periods. If the nominal annual rate is compounded monthly, then the monthly rate is the annual nominal rate divided by 12 and the number of periods is years × 12.
If the problem gives an effective annual rate (APY/AER) instead, do not divide it by 12 as though it were nominal. An effective rate already contains the annual compounding effect. The calculator converts that one-year growth factor into an equivalent periodic factor for its timeline.
2. Grow the starting principal
The starting amount is a single lump sum. With a monthly periodic rate, its future value is:
This part receives the maximum amount of time in the model because the money is present for every period.
3. Calculate the future value of the contribution stream
Equal contributions made at the end of each month form an ordinary annuity. Their future value is:
Why is this different from simply multiplying PMT by the number of months? Because the earliest contribution earns interest for many periods while the final contribution is deposited at the end and has essentially no time to grow inside the model. If equal contributions are made at the beginning of each period instead, the annuity stream receives one additional period of growth; for a regular monthly annuity this is the ordinary-annuity result multiplied by (1 + i).
4. Combine the two future values, then separate your money from interest
Your own money is calculated independently:
The modelled interest is therefore the amount left after subtracting total contributed money from the projected final balance. The interest share can then be expressed as a percentage of the final balance. This distinction is important in finance because a large account balance does not mean the same thing as a large investment return: part of the balance may simply come from larger or more frequent deposits.
5. Worked student exercise
Problem: Start with $5,000, contribute $150 at the end of each month, use a 4.8% nominal annual rate compounded monthly and project 8 years. Before revealing the answer, estimate whether interest will represent more or less than one quarter of the final balance.
For this problem, the monthly rate is 4.8% ÷ 12 = 0.4%, or 0.004 as a decimal, and the number of monthly periods is 8 × 12 = 96. Solve the starting-principal future value and the ordinary-annuity future value separately, add them, then subtract the $19,400 of total contributed money.
- Periodic rate: 4.8% ÷ 12 = 0.4% per month = 0.004.
- Number of periods: 8 × 12 = 96 months.
- Starting principal: 5,000 × (1.004)96 ≈ $7,335.11.
- End-of-month contributions: 150 × [((1.004)96 − 1) ÷ 0.004] ≈ $17,513.30.
- Projected final balance: $7,335.11 + $17,513.30 ≈ $24,848.41.
- Total money contributed: $5,000 + (150 × 96) = $19,400.00.
- Modelled interest: $24,848.41 − $19,400.00 = $5,448.41.
- Interest share: $5,448.41 ÷ $24,848.41 × 100 ≈ 21.9%.
6. How to check your own answer
Use three checks. First, the final balance must be at least as large as total contributions when the rate is non-negative. Second, the contribution stream should be worth more than the raw sum of contributions when the rate is positive, but it should not grow as much as if every contribution had been invested for the full eight years. Third, changing the contribution timing from end to beginning should increase the result when the rate is positive, because every deposit receives one additional period of growth. These checks do not replace the formula, but they are excellent at catching sign, rate and timing errors.
What this calculator does not model
The projection assumes the entered rate can be represented consistently across the whole term. It does not model changing market returns, changing bank rates, deposits on exact calendar dates, taxes, fees, inflation, currency movements, withdrawal rules or product-specific balance methods.
For nominal-rate mode, the calculator first derives the one-year effective growth implied by the chosen compounding frequency and then uses an equivalent monthly growth factor for the contribution timeline. This keeps monthly, quarterly and annual contributions comparable while avoiding a false claim that every provider posts interest in exactly the same way.
Use the result as an educational or planning estimate, not as a guarantee, investment recommendation or substitute for the terms of a specific financial product.
Continue exploring Finance
This calculator answers a forward-growth question: what could this amount grow to under these assumptions? Other Finance tools will solve different problems, such as the contribution required for a target or the payment required for a loan.