Savings Plan Calculator: Future Value With Deposits
Calculate the future value of a savings plan from a starting amount plus regular deposits, with your choice of contribution and compounding frequency.
Savings Plan Calculator
Documentation
Savings Plan Calculator
A savings plan calculator estimates how much a savings or investment account will be worth after a chosen number of years. It combines a one-time starting deposit with a regular contribution made monthly, quarterly, or annually, and grows both with compound interest.
What the calculator does
The calculator takes seven inputs: the initial deposit, the regular contribution, how often contributions are made (monthly, quarterly, or annually), whether each contribution lands at the beginning or the end of its period, the annual interest rate, how often interest compounds, and the number of years the money grows.
It returns three figures: the future value (the ending balance), the total contributions (the initial deposit plus every regular deposit), and the total interest earned (the difference between the two). A chart shows the balance at the end of every contribution period.
The initial deposit can be $0 to $1 trillion and the contribution $0 to $1 billion per period. The interest rate can be 0% to 100%. The number of years must be greater than 0 and at most 100. At least one of the deposit and the contribution must be above $0.
How to calculate the future value of a savings plan
Two standard results are combined, both described in the Wikipedia articles "Future value" and "Annuity".
The starting deposit grows by compound interest alone:
FV(deposit) = P₀ × (1 + i)ˣ
The stream of regular deposits grows as an annuity:
FV(contributions) = PMT × (1 + i)ˣ⁻ᴺ × A
- P₀ is the initial deposit.
- PMT is the regular contribution.
- i is the interest rate for one contribution period.
- x is the horizon measured in contribution periods (years × periods per year).
- N is the number of deposits actually made.
- A is the annuity factor, the future value of $1 deposited each period for N periods.
The annuity factor depends on when deposits land:
| Timing | Name | A |
|---|---|---|
| End of period | Ordinary annuity | ((1 + i)ᴺ − 1) / i |
| Beginning of period | Annuity due | ((1 + i)ᴺ − 1) / i × (1 + i) |
A deposit at the beginning of each period earns interest for one extra period, which is where the extra (1 + i) comes from. When the rate is 0%, the annuity factor is N: the deposits add up with no growth.
The future value is the sum of the two parts. Total interest is the future value minus everything paid in.
When compounding and contributions have different frequencies
Interest may compound more or less often than deposits are made, for example monthly compounding with quarterly deposits. The calculator converts the nominal annual rate r, compounded n times per year, into the effective rate for one contribution period (see the Wikipedia article "Effective interest rate"):
i = (1 + r/n)^(n/m) − 1
where m is the number of contributions per year. With a 5% annual rate compounded monthly and quarterly deposits, i = (1 + 0.05/12)³ − 1 ≈ 1.2552% per quarter. When the two frequencies match, i is r/n directly.
Worked example
A plan starts with $1,000 and adds $100 at the beginning of every month for 10 years at a 5% annual rate, compounded monthly. These are the calculator's default values.
- Periods per year m = 12, so the horizon is x = 120 periods and N = 120 deposits.
- The monthly rate is i = 0.05 / 12 ≈ 0.0041667.
- Growth factor: (1 + i)¹²⁰ ≈ 1.647009.
- Initial deposit: $1,000 × 1.647009 ≈ $1,647.01.
- Annuity factor (ordinary): (1.647009 − 1) / 0.0041667 ≈ 155.282279. Deposits land at the beginning of each month, so multiply by (1 + i): 155.929289.
- Contributions: $100 × 155.929289 ≈ $15,592.93.
- Future value: $1,647.01 + $15,592.93 = $17,239.94.
Total contributions are $1,000 + 120 × $100 = $13,000, so total interest is $17,239.94 − $13,000 = $4,239.94. With the same plan but deposits at the end of each month, the future value is $17,175.24, about $65 less.
A second example with end-of-month deposits: $5,000 initial, $200 per month, 6% compounded monthly, 20 years. Here (1.005)²⁴⁰ ≈ 3.310204, the deposit grows to $16,551.02, the annuity factor is 462.040895, and the contributions grow to $92,408.18. The future value is $108,959.20: $53,000 paid in and $55,959.20 of interest. This matches the U.S. Securities and Exchange Commission's compound interest calculator on investor.gov, which the tool's engine was checked against.
Conventions this calculator uses
Deposits default to the beginning of the period. Most real savings plans debit the account at the start of each month, so the default is an annuity due. Many textbooks and calculators assume an ordinary annuity instead; the timing option switches between the two.
Fractional years count deposits by timing. Over 2.5 years of annual deposits, an end-of-period plan makes 2 deposits (only completed years pay) while a beginning-of-period plan makes 3 (each year entered pays at its start). Every deposit made, and the initial sum, still grows to the exact horizon, including the final partial period.
Results are nominal. No inflation, tax, or fee is subtracted. The future value is what the account statement would show, not its purchasing power.
Rounding happens once, at the end. The future value and total contributions are each rounded to the cent, and total interest is their difference, so the three displayed figures always add up exactly.
Frequently asked questions
What is the future value of a savings plan? It is the account balance at the end of the plan: the starting deposit and every regular deposit, each grown by compound interest from the moment it was paid in until the end.
Does contributing at the beginning of the month really matter? Yes, a little. Each deposit earns one extra period of interest, which multiplies the contribution part of the balance by (1 + i). In the default example the difference over 10 years is $64.70.
Why does compounding frequency change the result? More frequent compounding credits interest sooner, so interest starts earning interest sooner. The calculator folds this into the effective per-period rate i = (1 + r/n)^(n/m) − 1, so any mix of compounding and contribution frequency is handled exactly.
What happens at a 0% interest rate? The future value is just the sum of all money paid in. The default plan at 0% ends at exactly $13,000 with $0 interest.
Does the calculator account for inflation or taxes? No. All results are nominal dollar amounts. To estimate purchasing power, a lower "real" rate can be entered instead, but the tool does not accept negative rates.
Why is total interest the future value minus total contributions? Interest is every dollar in the account that was not paid in. Since deposits are counted in total contributions, whatever remains of the future value must have come from compounding.
References
- "Future value." Wikipedia, https://en.wikipedia.org/wiki/Future_value.
- "Annuity." Wikipedia, https://en.wikipedia.org/wiki/Annuity.
- "Effective interest rate." Wikipedia, https://en.wikipedia.org/wiki/Effective_interest_rate.
- "Compound Interest Calculator." U.S. Securities and Exchange Commission, Investor.gov, https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator.