Future Value
Future value is the amount a sum of money can become after a specified number of interest-bearing periods. A deposit today and the balance available later are different amounts because the money has time to earn a return. That return may come from a savings account, a certificate of deposit, a bond holding with reinvested proceeds, or a longer-term investment. Future value connects a starting balance, a rate of growth and a length of time in one calculation.
The simplest example starts with $10 and earns 6% for one year, with no further deposits. Interest is $10 × 0.06 = $0.60, so the future value is $10.60. The original ten dollars remain part of the balance; sixty cents are the additional return. If the money stays invested for another year at the same rate, interest applies to $10.60 rather than just $10. The second year's interest is $0.636, bringing the unrounded balance to $11.236.
A future value is a projection under stated assumptions, not a promise that an investment will deliver that amount. The calculation assumes that each period earns the entered rate and that deposits occur on the selected timetable. Actual products can have fees, taxes, changing rates, withdrawal restrictions or market losses. Comparing a projection with the terms of a real account is therefore as important as calculating the number itself.
The Time Value of Money
Money available now has opportunities that money arriving later does not. It can earn interest, reduce debt, or fund something immediately. This principle is called the time value of money. Future value moves an amount forward through time, while present value moves a future amount backward to an equivalent amount today. Both use the same interest rate and the same period definition, so they are two directions of one relationship.
The five familiar quantities are PV, the starting or present amount; FV, the ending amount; I/Y, the interest or yield rate; N, the number of periods; and PMT, a recurring payment. Mortgages, car loans, credit-card repayment plans and retirement saving all depend on those quantities. A borrower and a saver have different purposes, but both must understand when cash moves and how interest changes the balance between payments.
For example, an amount due in five years is worth less today when a positive discount rate is used, because a smaller sum invested now could grow to cover it. Conversely, the future balance of a savings plan exceeds the money deposited when interest is positive. The Present Value Calculator focuses on discounting. The Finance Calculator explores the wider relationship among all five financial quantities.
Understanding the Inputs
Number of Periods (N)
A period is one interval during which interest compounds. It need not be a year. Ten annual periods mean ten years; ten monthly periods mean ten months. Keep the rate and recurring deposit expressed for that same interval. When the period is monthly, use a monthly rate and a monthly deposit. A positive fractional number of periods includes a final partial interval, rather than rounding the horizon to a whole period.
Starting Amount (PV)
The starting amount is the balance present before the first modeled period. It may be an existing savings balance or a new lump sum. It is separate from the recurring deposit. Entering $1,000 here and $100 as PMT means the plan starts with $1,000 and then adds $100 each complete period. Setting the starting amount to zero models building a balance entirely through regular contributions.
Interest Rate (I/Y)
The rate applies to each compound period in this calculation. Six means 6%, or 0.06 in a formula, not 600%. A zero rate means the balance changes only through deposits or withdrawals. A negative rate models a repeated loss in value, with the same timing rules. A rate greater than −100% keeps fractional compounding mathematically defined for the ordinary financial model used here.
Periodic Deposit (PMT)
PMT is the constant contribution made in each complete period. A positive amount adds money; a negative amount withdraws money. Zero leaves only the starting amount growing or shrinking. The calculation does not assume that contributions rise with inflation or wages. If contributions change materially over time, divide the plan into separate stages, carrying the ending balance of one stage into the starting amount of the next.
Future Value Formulas
Let P be the starting amount, D the periodic deposit, i the interest rate written as a decimal, and n the number of complete periods. For a single lump sum, each period multiplies the previous balance by 1 + i. Repeating that process gives the compound-growth formula:
FV = P × (1 + i)n
When deposits arrive at the end of each period, the first deposit earns interest for n − 1 periods, the second for n − 2, and the last earns none before the horizon ends. Adding this geometric series produces the ordinary-annuity formula:
FV = P × (1 + i)n + D × [(1 + i)n − 1] ÷ i
When deposits arrive at the beginning, every deposit earns one extra period of interest. Only the recurring-deposit portion receives the extra factor; the initial lump sum has the same growth horizon in both cases:
FV = P × (1 + i)n + D × [(1 + i)n − 1] ÷ i × (1 + i)
At zero interest the formula involving division by i is replaced by its limit: FV = P + nD. For a fractional horizon, complete periods follow the selected deposit timing, and the remaining fraction compounds the balance by (1 + i) raised to that fraction. No additional recurring deposit is added in that partial interval.
Beginning or End of Each Compound Period
End-of-period contributions are commonly called an ordinary annuity. Beginning-of-period contributions are an annuity due. The difference is the amount of time each deposit remains invested. A contribution made before interest is calculated participates in that period's growth. One made after interest is calculated waits until the next period before earning interest.
With a positive rate and positive deposits, beginning payments create a larger future value. With a negative rate, depositing earlier exposes the contribution to one more interval of loss, so the advantage reverses. When the rate is zero, timing has no effect on the ending amount. Withdrawals also require care: taking money out earlier removes more money from the interest-bearing balance sooner.
Worked Examples
A Starting Balance Plus Regular Deposits
The default plan starts with $1,000, adds $100 at the end of each of ten periods, and earns 6% per period. The lump sum grows to $1,790.85. The recurring deposits grow to $1,318.08, including their earned interest. Together these produce a future value of $3,108.93. Cash supplied to the plan totals $2,000: the original $1,000 plus ten $100 deposits. The remaining $1,108.93 is accumulated interest.
Move those same contributions to the beginning of each period and the future value becomes $3,188.01. The first period then starts with $1,100 after the deposit, earns $66 and ends at $1,166. The difference of $79.08 arises entirely from the extra earning time assigned to the deposits. Neither the starting balance nor the amount contributed has changed.
A Shorter Plan
Start with $250, add $50 at the end of each of three periods and earn 4% per period. The first ending balance is $310. The next becomes $372.40, and the final balance is $437.30. Regular deposits total $150, making total supplied money $400. Interest contributes the remaining $37.30. Short horizons keep the compounding effect modest, but the same rule continues to operate over longer plans.
Zero Growth and Negative Growth
Starting with $1,000 and adding $100 over three periods at 0% gives $1,300, regardless of payment timing. At −5% over five periods with end deposits, the plan ends at $1,226.22. Although deposits add $500, repeated losses remove $273.78. A rising ending balance does not always mean an investment earned a positive return: new contributions can conceal losses on the existing money.
Reading the Results and Schedule
Future Value is the projected balance at the end of the horizon. Total Periodic Deposits counts the recurring cash contributions, excluding the starting amount. Total Interest is the ending balance less the initial balance and all deposits. The result row labeled PV (Present Value) discounts the entire projected ending balance to today at the entered rate. Because this includes the value of future deposits, it is not necessarily the same as the starting amount entered in the form.
In the default example, the discounted present value is $1,736.01. This is the amount that, invested as a single lump sum at 6% for ten periods, would grow to the same $3,108.93 ending balance. It combines the original $1,000 with the discounted value of the future recurring deposits. The distinction avoids confusing a present-equivalent total with the actual cash already available.
The schedule traces every period. For end payments, interest applies to the start balance, and the deposit is added afterward. For beginning payments, the displayed start balance already includes that period's deposit, matching the interest-bearing balance. Deposit is shown separately to identify the cash contribution, not to instruct you to add it a second time. End balance becomes the basis for the next period.
The circular chart separates the starting amount, recurring deposits and accumulated interest. The stacked schedule chart shows how these contributions develop over time. Negative interest or withdrawals can create negative chart components; those represent reductions rather than additional wealth. Money amounts are displayed to two decimal places, but intermediate calculations retain precision, so adding individually rounded rows may differ by a cent from the unrounded total.
Rates, Inflation, Taxes and Investment Risk
Match rate frequency carefully. A nominal annual rate compounded monthly is usually divided by twelve to obtain the monthly rate, while an effective annual yield requires the conversion i = (1 + annual yield)1/12 − 1. These are different conventions. The product's published terms determine which conversion is appropriate. The Interest Calculator offers broader compounding choices when the plan needs them.
A projected dollar amount is nominal: it does not automatically account for inflation. If prices rise, the same number of future dollars buys less. At a constant inflation rate f over n periods, the future balance's purchasing power in today's money is FV ÷ (1 + f)n. Fees and taxes can also reduce the return that remains invested. A conservative comparison may therefore use a lower net rate, but a single adjustment cannot represent every possible tax treatment or changing charge.
Market returns are not constant. Two investments with the same average reported return can end differently when contributions or withdrawals occur along different return paths. This calculation is best used for transparent scenarios and comparisons, not as a probability forecast. Considering a cautious rate alongside a more optimistic one can reveal how dependent a saving goal is on growth rather than contributions.
Frequently Asked Questions
Does a period have to be a year?
No. It can be a month, quarter, year or another consistent interval. The rate and deposit must refer to that same interval. Mixing an annual rate with monthly periods would overstate growth unless the rate is converted first.
Why is the PV result different from my starting amount?
The result discounts the whole future balance, including the accumulated effect of recurring deposits. The starting amount is only the cash present at the beginning. They agree for a lump-sum-only plan with no additional cash flows.
Can I calculate without making regular deposits?
Yes. Set the periodic deposit to zero. The result then follows the single-lump-sum compound-growth formula. Payment timing has no effect because there are no recurring contributions to move.
What happens when the interest rate is zero?
The balance equals the starting amount plus the total deposits. Interest is zero and beginning versus end timing makes no difference. This also provides a useful check on whether the entered periods and deposit amount are sensible.
Can the calculator show losses or withdrawals?
Yes. A negative rate models losses, and a negative periodic deposit models withdrawals. A negative ending balance is a mathematical result indicating that the modeled withdrawals exceeded available money; it does not mean a real savings account automatically provides an overdraft.
How are fractional periods handled?
The balance compounds through the last fractional interval, but recurring deposits are counted only for complete periods. For example, 2.5 periods at the default rate and amounts produce two deposits, followed by half a period of growth, giving $1,368.91.
Is this the same as a guaranteed investment return?
No. The result follows the assumptions entered. A guarantee depends on a real product's contract and issuer, while a market investment can fluctuate. Taxes, account fees and inflation are not separately deducted here.
Why does interest tend to grow in the schedule?
At a positive rate, interest is calculated on an increasingly large balance when prior interest remains invested and deposits continue. The same rate multiplied by more money produces a larger interest amount. This is the practical meaning of compound growth.