Solve for any time-value-of-money variable: PV, FV, PMT, rate, or N using the TVM framework.
Negative if you pay it out
0 for a lump sum
Pick the value you want to solve for, then enter the other four. This works like a financial calculator (or Excel’s FV, PV, PMT, RATE and NPER functions), using the cash-flow sign convention: money you pay out — a deposit, an investment, a loan payment — is negative; money you receive — a loan you take out, a final balance you withdraw — is positive.
Example: investing $10,000 now (PV = −10000) and adding $100 a year (PMT = −100) at 7% for 10 years gives a positive FV — the amount you could withdraw. For a $10,000 loan, enter PV = 10000 and FV = 0; the payment comes back negative because you pay it.
The rate and number of periods must use the same period: for monthly payments, enter the monthly rate (annual ÷ 12) and the number of months.
PV·(1+i)ⁿ + PMT·(1 + i·t)·[(1+i)ⁿ − 1] / i + FV = 0i = rate per period, n = number of periods, t = 0 for payments at the end of each period or 1 for the beginning. When i = 0 the equation becomes PV + PMT·n + FV = 0. The interest rate is found numerically because the equation cannot be rearranged for i.
Time value of money is the principle that a dollar today is worth more than a dollar in the future because it can earn interest. The TVM equation links present value, future value, regular payments, the interest rate and the number of periods, so knowing any four lets you solve for the fifth.
This calculator uses the standard cash-flow sign convention. A negative result means money you pay out (for example a loan payment or the deposit needed today); a positive result means money you receive.
An ordinary annuity pays at the end of each period (most loans). An annuity due pays at the beginning (rent, many savings plans). Beginning-of-period payments earn one extra period of interest, so they produce a larger future value.
Convert both to the same period: divide the annual rate by 12 and multiply the years by 12. For example, a 6% loan over 5 years with monthly payments uses I/Y = 0.5 and N = 60.
PV (Present Value) is what money is worth today. FV (Future Value) is what it will be worth later. PMT (Payment) is the periodic cash flow. Rate is the interest or discount rate per period. N is the total number of periods. Knowing any four allows you to solve for the fifth. This calculator handles all five scenarios.
Did you know?
Every financial transaction — loans, mortgages, bonds, annuities, leases, and investments — can be analyzed using just five TVM variables: Present Value, Future Value, Payment, Interest Rate, and Number of Periods.
Time Value of Money (TVM) is one of the most fundamental concepts in finance, formalized by Irving Fisher in his 1930 book "The Theory of Interest." The concept that money available today is worth more than the same amount in the future due to its potential earning capacity underpins virtually all financial decision-making.
Net Present Value (NPV) analysis, based on TVM, is the standard method used by corporations to evaluate capital investment decisions worth billions of dollars.
The TVM formula is used by actuaries to calculate insurance premiums, pension obligations, and structured settlements.
Bond pricing is entirely based on TVM — a bond's price is simply the present value of all future coupon payments plus the face value at maturity.