The Finance Calculator solves time-value-of-money problems. Choose the variable you want to find - future value (FV), present value (PV), periodic payment (PMT), interest rate (I/Y), or number of periods (N) - fill in the other four, and click Calculate.
The finance calculator is a versatile time-value-of-money (TVM) solver that handles the five core variables behind nearly every financial decision: the number of periods (N), the interest rate per year (I/Y), the present value (PV), the periodic payment (PMT), and the future value (FV). Provide any four of these values and the calculator solves for the fifth. This is the same fundamental calculation built into financial calculators like the HP 12C and TI BA II Plus, and it underpins loans, mortgages, savings plans, annuities, bonds, and investment projections.
Use the tabs to select which variable you want to solve for - FV, PMT, I/Y, N, or PV - then enter the remaining values. The calculator also shows the sum of all periodic payments, the total interest, a value-over-time chart, and a period-by-period schedule.
The time value of money is the foundational concept of finance: a dollar today is worth more than a dollar in the future, because money available now can be invested to earn a return. Conversely, a dollar promised in the future is worth less than a dollar today. The TVM framework quantifies this relationship using an interest (or discount) rate, allowing you to compare amounts of money across different points in time on an equal footing.
Every TVM problem connects a present value, a stream of equal periodic payments, and a future value through a compounding interest rate over a number of periods. The finance calculator links all five together with a single equation.
The finance calculator uses the standard cash-flow sign convention used by all financial calculators: money flowing in is positive and money flowing out is negative (or vice versa, as long as you are consistent). For example, if you deposit $20,000 today (an inflow to the account, shown as a positive PV) and withdraw $2,000 each year (an outflow, shown as a negative PMT), the resulting FV reflects the remaining balance. This is why the default example uses PV = 20000 (positive) and PMT = -2000 (negative). If your result appears with an unexpected sign, check that your inflows and outflows have opposite signs.
All five variables are linked by a single equation. For payments made at the end of each period (an ordinary annuity):
PV × (1 + i)N + PMT × [((1 + i)N − 1) / i] + FV = 0
Here i is the interest rate per period, derived from the annual rate and your compounding settings. The calculator rearranges this equation algebraically to solve for FV, PV, or PMT directly, and uses numerical methods to solve for I/Y or N when those are the unknowns.
Worked example (FV): With N = 10, I/Y = 6%, PV = $20,000, and PMT = -$2,000 (paid at the end of each year), the future value is $20,000 × 1.0610 + (-$2,000) × [(1.0610 − 1) / 0.06] = $35,816.95 − $26,361.59 = $9,455.36, shown as FV = -$9,455.36. The total interest earned is $9,455.36 and the sum of payments is -$20,000.
The PMT made at the setting determines whether payments occur at the end of each period (an ordinary annuity, the default) or at the beginning of each period (an annuity due). With an annuity due, each payment has one extra period to earn interest, so the future value is higher. Rent and lease payments are typically annuities due (paid at the start of the period), while most loan payments are ordinary annuities (paid at the end). In the equation, the payment term is simply multiplied by (1 + i) for an annuity due.
Two settings control how interest compounds relative to how often payments are made:
When C/Y differs from P/Y, the calculator converts the nominal annual rate into the correct effective rate per payment period using the formula i = (1 + (I/Y ÷ C/Y))(C/Y ÷ P/Y) − 1. When P/Y = C/Y = 1, this simplifies to i = I/Y, the annual rate itself.
Enter the loan amount as PV, set FV to 0 (the loan is fully paid off), enter the rate and number of payments, and solve for PMT to find your payment. Or enter a payment you can afford and solve for N to see how long the loan will take, or for PV to see how much you can borrow.
To project a savings plan, set PV to your starting balance, PMT to your recurring contribution, the rate and number of periods, and solve for FV to see your ending balance. Solve for PMT to find how much you must save each period to reach a goal.
Estimate how large a nest egg you need (PV at retirement) to support a given withdrawal (PMT) over a number of years, or how long your savings will last by solving for N.
Solve for I/Y to find the implied rate of return that connects an initial investment, periodic cash flows, and a final value - useful for comparing opportunities on a consistent basis.
Present value answers "what is a future amount worth today?" by discounting it back at the interest rate. Future value answers "what will an amount today grow to?" by compounding it forward. They are two sides of the same coin: discounting is the reverse of compounding. A higher interest rate increases future value (money grows faster) but decreases present value (future money is discounted more heavily). Understanding both is essential for valuing investments, loans, and any decision involving cash flows over time.
Compounding - earning interest on previously earned interest - is the engine behind long-term wealth building. The longer the time horizon and the higher the rate, the more dramatic the effect. This is why starting to invest early is so powerful: even modest contributions compound into large sums over decades. The finance calculator makes this concrete by letting you see exactly how a present value, a stream of payments, and a rate combine into a future value over any number of periods.
It solves any one of the five time-value-of-money variables - future value (FV), present value (PV), periodic payment (PMT), interest rate per year (I/Y), or number of periods (N) - given the other four. Select the variable using the tabs.
The calculator follows the standard cash-flow sign convention: money flowing in one direction is positive and money flowing the other way is negative. For the math to work, inflows and outflows must have opposite signs. A negative result simply indicates the opposite cash-flow direction from your positive inputs.
I/Y is the nominal annual interest rate you enter. The lowercase i is the effective rate per compounding/payment period that the calculator derives from I/Y using your P/Y and C/Y settings. When P/Y = C/Y = 1, the two are equal.
In an ordinary annuity, payments occur at the end of each period; in an annuity due, they occur at the beginning. Because beginning-of-period payments earn interest for one extra period, an annuity due produces a larger future value. Use the "PMT made at the" setting to switch between them.
Yes. Enter the loan amount as PV, set FV to 0, enter the annual rate as I/Y and the number of payments as N (with P/Y set to your payment frequency), then solve for PMT to find your payment. You can also solve for N or PV to explore different scenarios.
When you solve for I/Y, there is no simple algebraic formula, so the calculator uses a numerical method (iteration) to find the rate that makes the present value, payments, and future value balance to zero, then converts it to an annual rate.