Time Value of Money Calculator (solve for PV, FV, PMT, N or rate)

Understanding the time value of money calculator — concept and principle

The time value of money links five quantities: present value, payment, future value, interest rate and number of periods. Given any four, this calculator solves for the fifth. It works for savings plans, loans, annuities and single sums.

The starting sum grows to $18,193.97 and the payments to $32,775.87: $50,969.84 in total, $16,969.84 of it interest.

How it is calculated

FV = PV(1 + i)^N + PMT(1 + i·t)((1 + i)^N − 1) ÷ i

i = annual rate ÷ periods per year; N = years × periods per year.
t = 1 for payments at the start of each period, 0 at the end.
PV and PMT are solved directly, N with logarithms, and the rate numerically.
Sign convention: money that grows the balance is positive, money taken out is negative. For a loan, enter the amount borrowed as PV, repayments as a negative PMT and the remaining balance (often 0) as FV.

The principle

A unit of money today can earn interest, so it is worth more than the same unit later. Compounding grows a single sum by (1 + i) each period, and a stream of equal payments grows as a geometric series. Combining both gives one equation that underlies loans, mortgages, pensions and savings plans. Because the equation is the same, one calculator can solve any of the five unknowns.

Worked example

Default inputs: solve for FV; PV 10,000 USD; PMT +200 USD; 6% a year; 10 years; 12 periods a year; payments at the end.

i = 6% ÷ 12 = 0.5%; N = 120.
PV grows to 10,000 × 1.005^120 ≈ 18,193.97 USD.
Payments grow to 200 × (1.005^120 − 1) ÷ 0.005 ≈ 32,775.87 USD.
FV = 18,193.97 + 32,775.87 = 50,969.84 USD.
Total payments = 200 × 120 = 24,000.00 USD; interest earned = 50,969.84 − 10,000 − 24,000 = 16,969.84 USD.

Each point is the calculator re-run with only “Number of years” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Number of years	Solved value
2.5	$18,070.00
5	$27,442.51
7.5	$38,327.73
10	$50,969.84
12.5	$65,652.38
15	$82,704.68
20	$125,510.22

How to read the result

Interest earned shows how much of the final amount comes from compounding rather than from your own money. When solving for a rate, the result is a periodic rate converted to an annual nominal rate; compare it with offers on the same basis. Rates here are nominal and compound once per period.

Common mistakes

Getting the signs wrong, for example entering a loan repayment as positive.
Mixing annual rates with monthly periods without setting periods per year.
Choosing payments at the start when they occur at the end, or the reverse.
Expecting a rate solution when the cash flows never change sign.

Keep in mind: Assumes a constant rate and equal payments; taxes and fees are not included. This is not financial advice.

Frequently asked questions

What are the five time value of money variables?

Present value, payment, future value, interest rate and number of periods.

Why do some values need a negative sign?

The sign shows the direction of the cash flow, so the equation can tell deposits from withdrawals.

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

Payments at the end of each period versus at the start; an annuity due earns one extra period of interest.

Sources: Brigham & Houston, Fundamentals of Financial Management (time value of money) · CFA Institute, Quantitative Methods: The Time Value of Money

Checked 9 Nov 2026. Time-value-of-money equation for a lump sum plus an ordinary annuity or annuity due: R. A. DeFusco et al., “Quantitative Investment Analysis”, 4th ed. (CFA Institute / Wiley, 2020), The Time Value of Money.

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