Time Value of Money Calculator
The time value of money (TVM) principle states that a dollar today is worth more than a dollar in the future because it can earn interest now. This calculator solves for any one of the five core TVM variables: present value, future value, interest rate, number of periods, or periodic payment. Choose lump-sum or annuity mode, pick ordinary or annuity-due timing, and select from seven compounding frequencies. Results update instantly as you type.
What is the time value of money?
The time value of money (TVM) is the foundational idea that a sum of money available today is worth more than the same sum in the future. The reason is simple: money received now can be invested to earn interest, so it grows. Conversely, future money must be discounted back to the present to find its equivalent current worth. This concept underpins nearly every financial decision, from evaluating a business investment and pricing a bond, to planning retirement savings and choosing between a lump-sum lottery prize and annual installments.
The five TVM variables and how to use this calculator
Every TVM problem has five variables: Present Value (PV), Future Value (FV), interest rate (r), number of periods (n), and periodic payment (PMT). If you know four of them, you can solve for the fifth. Use the "Solve for" selector to choose your unknown, then fill in the remaining fields. For a lump-sum investment with no recurring payments, leave PMT at 0. For a savings plan or loan, enter a positive PMT for deposits or a negative PMT for withdrawals. Choose the compounding frequency that matches the actual investment or loan (most bank accounts and loans compound monthly), and switch between ordinary annuity (payments at period end) and annuity due (payments at period start, like rent) using the payment timing selector.
Key formulas
Lump-sum only: FV = PV x (1 + r/m)^(m x t), where r is the nominal annual rate and m is the number of compounding periods per year. For continuous compounding: FV = PV x e^(r x t). With periodic payments (ordinary annuity): FV = PV x (1+r)^n + PMT x ((1+r)^n - 1) / r. For an annuity due, multiply the annuity component by (1 + r). The effective annual rate (APY) = (1 + r/m)^m - 1, or e^r - 1 for continuous compounding. Present value is the inverse: PV = FV / (1 + r/m)^(m x t). Solving for rate or periods requires numerical methods (bisection iteration) because those equations cannot be rearranged into a closed form when PMT is non-zero.
Practical applications
Retirement planning: use the FV solve to find how a lump sum plus monthly contributions grows over 30 years. College savings: use PV to find how much you need to invest today to reach a tuition target. Loan analysis: use PMT to find the monthly payment that retires a balance at a given rate. Break-even timeline: use the periods solve to find when an investment reaches a target. Rate comparison: enter known PV, FV, and periods to discover the implied yield of an investment or the effective cost of a loan. In all cases, the growth chart lets you see the trajectory year by year, and the breakdown bar shows how much of the final balance is your own money versus earned interest.
Compounding frequency and effective annual rate (APY)
| Compounding | Periods per year | Effective Annual Rate (APY) |
|---|---|---|
| Annually | 1 | 6.000% |
| Semi-annually | 2 | 6.090% |
| Quarterly | 4 | 6.136% |
| Monthly | 12 | 6.168% |
| Weekly | 52 | 6.180% |
| Daily | 365 | 6.183% |
| Continuous | inf | 6.184% |
For a 6% nominal annual rate, higher compounding frequency produces a higher effective yield.
Frequently asked questions
What is the difference between present value and future value?
Present value (PV) is what a future sum of money is worth in today's terms, after discounting for the time that must pass before you receive it. Future value (FV) is what a current sum will be worth at a later date, after earning interest over that time. They are two sides of the same equation: FV = PV x (1 + r)^n.
What is the difference between nominal rate and effective annual rate (APY)?
The nominal rate is the stated annual interest rate before accounting for compounding within the year. The effective annual rate (APY or EAR) is the actual annual yield after compounding is applied. For a 6% nominal rate compounded monthly, the EAR is (1 + 0.06/12)^12 - 1 = 6.168%. The more frequently interest compounds within the year, the higher the EAR relative to the nominal rate.
What is an ordinary annuity versus an annuity due?
An ordinary annuity has payments at the end of each period - this applies to most loans, mortgages, and bond coupon payments. An annuity due has payments at the beginning of each period - rent and lease payments are the most common example. Because an annuity-due payment is invested one period earlier, its future value is higher by a factor of (1 + r) compared to an ordinary annuity.
What does the Rule of 72 mean?
The Rule of 72 is a quick mental-math shortcut: divide 72 by the annual interest rate (as a whole number) to estimate how many years it takes money to double. At 6%, money doubles in roughly 72 / 6 = 12 years. The exact answer from the TVM formula is ln(2) / ln(1.06) = 11.9 years, so the rule is very close. It works best for rates between 2% and 20%.
How does compounding frequency affect the result?
More frequent compounding means interest is applied more often, so each period's interest also earns interest sooner. A 6% rate compounded daily produces a 6.183% effective annual yield, compared to exactly 6% when compounded just once per year. The difference grows with the rate and the time period. Continuous compounding - the mathematical limit of compounding every instant - gives e^r - 1 as the EAR.
Can I use this to calculate loan payments?
Yes. Select "Solve for: Periodic Payment (PMT)", enter the loan amount as Present Value, 0 as Future Value (because you want the balance to reach zero), the annual interest rate, and the number of years. Set compounding to "Monthly" and payment timing to "End of period (ordinary annuity)". The resulting PMT is the monthly payment. Enter it as a negative number conceptually (it is a cash outflow), but the calculator accepts the magnitude.