Time Value of Money Calculator
A dollar today isn't a dollar next year, and that's not just an old saying. Enter your amount, rate, term, and compounding frequency to see exactly what time is worth.
Quick answer: Time value of money uses FV = PV × (1 + i/n)^(n × t) to find future value, or the reverse to find present value. For example, $100 today at a 5% annual rate compounded yearly grows to $115.76 in three years. Enter your own numbers below for an exact result.
Your result will appear here.
What is the time value of money?
Time value of money, often shortened to TVM, is one of the foundational ideas in finance: a specific amount of money available today is worth more than that exact same amount received at some point in the future. The reason is simple. Money in hand today can be invested, deposited, or otherwise put to work earning a return, so by the time that future date arrives, today's money could have already grown into something larger.
This single concept underpins an enormous range of financial decisions, including retirement planning, loan structuring, bond pricing, and investment comparisons. It is sometimes referred to as discounted cash flow analysis when applied to valuing future income streams. Whether you're figuring out what a future payout is really worth today, or projecting what today's savings could become years from now, you're using time value of money either way.
The time value of money formula
For standard periodic compounding, the two core formulas are mirror images of each other:
Future Value: FV = PV × (1 + i / n)^(n × t)
Present Value: PV = FV ÷ (1 + i / n)^(n × t)
In both formulas, PV is present value, FV is future value, i is the annual interest rate, n is the number of compounding periods per year, and t is the term expressed in years. When compounding is continuous rather than periodic, the formulas shift to use the mathematical constant e, approximately 2.718:
Future Value (continuous): FV = PV × e^(i × t)
Present Value (continuous): PV = FV ÷ e^(i × t)
As a worked example, $100 invested today at a 5% annual interest rate, compounded once per year, for three years grows to $115.76. Plugging the numbers in directly: FV = 100 × (1 + 0.05/1)^(1 × 3) = 115.76. That $15.76 of growth is the time value of money made concrete.
Why compounding frequency changes your result
The same rate and term can produce noticeably different results depending on how often interest compounds. Every time interest compounds, it gets added to the balance and starts earning its own interest going forward. Compounding more frequently means more of those "interest on interest" moments happen within the same stretch of time.
Notice how the gap shrinks as frequency increases. Moving from annual to monthly compounding adds over $1,000 to this example over 20 years, but moving from daily all the way to continuous compounding, the theoretical maximum, adds only a few dollars. Diminishing returns kick in fast once you're compounding more than a few times a month.
Present value vs future value: two sides of one idea
Future value answers "what will this amount become?" Present value answers the reverse question, "what is that future amount actually worth right now?" Both rely on the exact same rate, term, and compounding frequency; the only difference is which direction you're moving along the timeline.
Present value calculations show up constantly in real decisions: comparing a lump-sum lottery payout against an annuity option, evaluating whether a future settlement offer is actually a fair deal today, or deciding how much to invest now to hit a specific future target. Future value calculations answer the more familiar question of how a current balance or investment is likely to grow.
Where time value of money shows up in real financial planning
TVM is not just an academic formula. It is the engine behind retirement projections, loan amortization schedules, bond pricing, and comparisons between different investment options. If you are mapping out a full retirement timeline rather than a single lump-sum projection, the Early Retirement Calculator applies this same underlying time value logic across your entire savings and withdrawal plan, rather than a single amount over a single term.
This calculator is built specifically for a single lump sum growing or discounting on its own. If your situation instead involves making the same contribution repeatedly, such as a fixed monthly deposit into a retirement account, the Future Value of Annuity Calculator is the more accurate tool, since it is built around a recurring stream of payments rather than a single starting amount.
A quick note on inflation
This calculator computes nominal time value, based purely on the stated interest rate, without separately factoring in inflation. Inflation quietly reduces the purchasing power of a future dollar amount even as the nominal number on paper keeps growing. For a rough real, inflation-adjusted estimate, subtract your assumed inflation rate from the interest rate before running the numbers here. A 6% nominal return with 3% inflation behaves closer to a 3% real return in terms of actual purchasing power.
Time Value of Money Calculator FAQs
What is the time value of money?
The time value of money is the financial principle that a specific amount of money available today is worth more than the same amount received at some point in the future, because money in hand today can be invested and earn a return between now and then. A dollar today, put into an interest-bearing account, becomes more than a dollar by next year, which is exactly why $100 today and $100 promised three years from now are not actually equal in value.
What is the formula this calculator uses?
For standard periodic compounding, future value is calculated as FV = PV × (1 + i/n)^(n × t), and present value is calculated as PV = FV ÷ (1 + i/n)^(n × t), where PV is present value, FV is future value, i is the annual interest rate, n is the number of compounding periods per year, and t is the term in years. For continuous compounding, the calculator instead uses FV = PV × e^(i × t) and PV = FV ÷ e^(i × t), where e is the mathematical constant approximately equal to 2.718.
What is the difference between present value and future value?
Present value answers the question, what is a future sum of money worth today, given a specific interest rate and time period? Future value answers the opposite question, what will today's money grow into after that same interest rate and time period? Both use the identical underlying relationship. Present value discounts a future amount backward in time, while future value compounds a present amount forward in time.
Why does compounding frequency change the result so much?
More frequent compounding means interest gets calculated and added to the balance more often, and each of those additions then earns its own interest sooner. Annual compounding only applies interest once a year, while monthly compounding applies it twelve times, and daily compounding applies it 365 times. Over short terms and modest rates the difference is small, but over longer terms and higher rates, switching from annual to daily or continuous compounding can add up to a noticeably larger final value.
What does continuous compounding actually mean?
Continuous compounding is the theoretical limit of compounding frequency, where interest is calculated and reinvested at every possible instant rather than at fixed intervals like monthly or daily. In practice, very few real financial products compound continuously, but it appears often in academic finance and options pricing because it produces a clean mathematical formula using the constant e. It also represents the mathematical ceiling for how much a given interest rate and term can grow an amount, even though daily compounding gets extremely close to it in practice.
Can I use this calculator for a loan instead of an investment?
Yes, the same present value and future value relationship applies to money owed just as much as money invested. A loan's present value is the amount borrowed today, and its future value at a given interest rate is what that debt would grow to if left completely unpaid and interest just kept compounding. This calculator is built around a single lump sum rather than a loan's regular payment schedule, so it works best for illustrating how a debt would grow, rather than modeling an actual amortizing loan payment plan.
Does this calculator account for inflation?
No, this calculator computes nominal time value of money based purely on a stated interest rate, term, and compounding frequency, without separately adjusting for inflation. To get a true inflation-adjusted, or real, future value, you would subtract an assumed inflation rate from the nominal interest rate before running the calculation, since inflation quietly erodes the purchasing power of whatever nominal amount you end up with.
How is this different from the Future Value of Annuity Calculator?
This calculator handles a single lump sum, one amount, growing or discounting over time at a given rate. The Future Value of Annuity Calculator instead handles a repeated series of equal payments made at regular intervals, such as a fixed monthly retirement contribution, and calculates what that whole stream of payments grows into over time. If you're depositing money once, use this tool. If you're contributing the same amount repeatedly, the annuity calculator is the more accurate fit.
This tool is for educational purposes only. Always verify important results with a qualified professional.
