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Business finance / Time Value of Money Calculator

Time Value of Money Calculator

Solve any time value of money problem: enter four of N, interest rate, present value, payment and future value, and the calculator finds the fifth, just like the TVM keys on a financial calculator. Use it for savings plans, loan payments, the price of a future sum today or the rate a deal really pays.

Enter a number from 0 to 10000

Total payment periods, e.g. 60 for five years of monthly payments.

%

Enter a number from -99 to 1000%

The yearly nominal rate. It is divided by the payments per year to get the rate per period.

$

Enter a number from -1000000000000 to 1000000000000

Money paid out is negative (a deposit), money received is positive (a loan you take).

$

Enter a number from -1000000000000 to 1000000000000

Same sign rule: −200 is $200 you pay in each period. Use 0 for a single lump sum.

Future value (FV)
$27,442.51
−$12,000.00total of payments
$5,442.51interest earned
6.168%effective yearly rate
N, number of periods · 5 years at 12 a year60
I/Y, annual rate · 0.5% per period6%
PV, present value−$10,000.00
PMT, payment · at the end of each period−$200.00
FV, future value$27,442.51
Net of all cash flows · PV + PMT × N + FV$5,442.51

Solved with PV × (1 + i)^N + PMT × (1 + i × 0) × ((1 + i)^N − 1) ÷ i + FV = 0, where i = 0.5% per period. Negative numbers are money paid out.

See breakdown

How the time value of money calculation works

  1. Choose what to solve for

    Pick FV, PV, PMT, the rate or N. The field you solve for is hidden; fill in the other four.

  2. Use signs for direction

    Money you pay out is negative and money you receive is positive. A $10,000 deposit is −10,000; the balance you collect later is positive. A loan you receive is +25,000 and its payments are negative.

  3. Set payments per year and timing

    The annual rate is divided by P/Y to get the rate per period, so a 6% rate with monthly payments is 0.5% a period. Rent and leases are often paid at the beginning (annuity due).

  4. The TVM equation

    PV × (1 + i)^N + PMT × (1 + i × t) × ((1 + i)^N − 1) ÷ i + FV = 0, with t = 1 for payments at the beginning. FV, PV, PMT and N come straight from the formula; the rate is found by trial until the equation balances.

Worked example. A business sets aside $10,000 today and adds $200 a month for 5 years (N = 60) at 6% a year, compounded monthly. Enter PV −10,000 and PMT −200 and solve for FV: the reserve grows to $27,442.51. Of that, $22,000.00 is its own money and $5,442.51 is interest. The effective yearly rate is 6.168%.

Time Value of Money FAQ

What is the time value of money?

A dollar today is worth more than a dollar later, because today's dollar can earn interest. The TVM equation links what money is worth now (PV), later (FV), the regular payments (PMT), the rate and the number of periods.

What is the time value of money formula?

PV × (1 + i)^N + PMT × (1 + i × t) × ((1 + i)^N − 1) ÷ i + FV = 0, where i is the rate per period and t is 1 for payments at the beginning of each period and 0 at the end. Without payments it reduces to FV = PV × (1 + i)^N.

Why do I get “No solution”?

Almost always a sign problem. If you put money in, PV and PMT are negative and the FV you get back is positive. If all the amounts have the same sign, no interest rate can make them balance.

How do I find the interest rate on a loan?

Choose “Interest rate”, enter the loan amount as a positive PV, the monthly payment as a negative PMT, FV 0 and the number of payments as N. $25,000 repaid at $500 a month for 60 months is a 7.4201% annual rate.

What is the difference between an ordinary annuity and an annuity due?

In an ordinary annuity payments come at the end of each period, like most loan payments. In an annuity due they come at the beginning, like rent, so each payment earns one more period of interest and the future value is higher.

How do I calculate the present value of an annuity?

Choose “Present value”, enter the payment you will receive as a positive PMT, the rate, N and FV 0. $1,000 a year for 10 years at 5% is worth $7,721.73 today; the answer shows as a negative PV because it is what you would pay for it.

What does P/Y mean?

Payments per year. The annual rate is divided by P/Y, and N counts payment periods, so 5 years of monthly payments is N = 60 with P/Y = 12.

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