TVM Calculator

Time Value of Money.

Note on Signs: TVM calculators use a cash-flow sign convention. Outflows (deposits, investments) are negative. Inflows (loans received, withdrawals) are positive.

Solve For:

Present Value (PV)Initial amount (e.g. -1000 for investment)

Future Value (FV)

Payment (PMT)Recurring amount per period

Number of Periods (N)Total number of payment periods

Annual Rate (I/Y) %Nominal annual interest rate

Compounding (C/Y)

Payments / Year (P/Y)

Payment Timing

TVM Calculator – Time Value of Money

Use this TVM Calculator (Time Value of Money) to solve for any one of the five core finance variables: Present Value (PV), Future Value (FV), periodic Payment (PMT), Number of Periods (N), or Annual Interest Rate (I/Y). It works for investments, savings plans, and loans where cash flows occur at regular intervals and a constant interest rate applies.

The calculator supports different compounding frequencies (annually, semi‑annually, quarterly, monthly, weekly, daily, or continuous), separate payment frequencies (P/Y), and both end‑of‑period and beginning‑of‑period payment timing (ordinary annuity vs annuity due).

How to use the TVM Calculator

Select “Solve For” and choose the unknown you want (FV, PV, PMT, N, or I/Y).
Enter the other four known values, including compounding periods per year (C/Y), payments per year (P/Y), and payment timing (end or beginning of period).
Click Calculate to compute the missing value and see the implied growth or cost over time.

Common examples:

Find how much a monthly SIP must be to reach a target savings goal.
Compute the future value of a lump‑sum investment with regular top‑ups.
Determine how long it will take to grow funds to a target amount at a given rate.
Solve the effective interest rate implied by a loan or investment with known cash flows.

Cash‑flow sign convention

TVM calculations use a consistent cash‑flow sign convention used in professional finance calculators.

Outflows (money you pay or invest) are negative.
Inflows (money you receive or withdraw) are positive.

Examples:

Investing ₹1,000 today and getting a positive future value later → PV = -1000, FV > 0.
Taking a loan today and making repayments over time → PV > 0 (loan proceeds), PMT < 0 (payments).

If all values are entered with the same sign, there is no real exchange of cash flows in or out, so the equation has no meaningful solution.

TVM variables explained

Present Value (PV): The current value of your money today, before interest and future payments.
Future Value (FV): The amount your money will grow to in the future, after compounding and payments.
Payment (PMT): The fixed recurring deposit or withdrawal made each period (for example, a monthly SIP or EMI).
Number of Periods (N): Total number of compounding/payment periods over the life of the investment or loan.
Annual Interest Rate (I/Y): The nominal yearly rate, which the calculator converts to an effective rate per period based on your chosen compounding and payment frequency.

When Payment Timing is set to “Beginning of Period (Annuity Due)”, each payment earns one extra period of interest compared with “End of Period (Ordinary Annuity)”, so for the same inputs, annuity‑due results are slightly higher.

What this calculator is useful for

You can use this TVM calculator to:

Plan savings: estimate how much to invest periodically to reach a future goal.
Evaluate investments: see how a lump sum grows under different rates and time horizons.
Understand loans: approximate the payment size or repayment time for a given loan amount and interest rate.
Explore “what‑if” scenarios by changing rate, time, or payment size and instantly seeing the impact on your results.

This tool assumes a constant interest rate, regular payment intervals, and no additional fees or taxes.

Formulas used in this TVM Calculator

This TVM Calculator uses standard time value of money formulas for single lump sums and annuities with compound interest, as taught in corporate finance and CFA‑level material. Below are the equations the calculator applies behind the scenes.

1. Single cash flow (PV ↔ FV)

For a single amount growing with compound interest:

Future value of a lump sum:
FV=PV×(1+i)NFV=PV×(1+i)N
Present value of a lump sum (discounting):
PV=FV(1+i)NPV=(1+i)NFV

Where:

PVPV = present value (value today)
FVFV = future value (value at the end)
ii = effective interest rate per period
NN = number of compounding periods

If you enter a nominal annual rate rr with mm compounding periods per year, the calculator converts it to the effective per‑period rate and total number of periods:

i=rm,N=m×ti=mr,N=m×t

Where tt is the number of years.

For continuous compounding, the classic time value of money formula is:

FV=PV×ert,PV=FV×e−rtFV=PV×ert,PV=FV×e−rt

2. Future value of an annuity (series of payments)

For a stream of equal payments PMT each period at a fixed rate ii, the calculator uses:

Ordinary annuity (payments at end of each period):
FVordinary=PMT×(1+i)N−1iFVordinary=PMT×i(1+i)N−1
Annuity due (payments at beginning of each period):
FVdue=PMT×(1+i)N−1i×(1+i)FVdue=PMT×i(1+i)N−1×(1+i)

When you also enter a non‑zero PV (initial lump sum), its future value is added using the single‑sum formula:

FVtotal=PV×(1+i)N+FVannuityFVtotal=PV×(1+i)N+FVannuity

3. Present value of an annuity

To discount a series of equal cash flows back to today, the calculator applies:

Ordinary annuity (end‑of‑period payments):
PVordinary=PMT×1−(1+i)−NiPVordinary=PMT×i1−(1+i)−N
Annuity due (beginning‑of‑period payments):
PVdue=PMT×1−(1+i)−Ni×(1+i)PVdue=PMT×i1−(1+i)−N×(1+i)

If you also enter a known future lump sum, it is discounted separately and added:

PVtotal=FV(1+i)N+PVannuityPVtotal=(1+i)NFV+PVannuity

4. Solving for N (number of periods)

When you choose “solve for N” and you only have a single PV and FV, the calculator rearranges the lump‑sum TVM formula:

From

FV=PV×(1+i)NFV=PV×(1+i)N

We get

N=ln⁡(FV/PV)ln⁡(1+i)N=ln(1+i)ln(FV/PV)

For more complex cases that include both PV and PMT, the calculator uses a numerical method (iteration) to find the NN that satisfies the full TVM equation.

5. Solving for interest rate (I/Y)

When the interest rate is the unknown, there is no simple closed‑form formula for the general case that includes PV, PMT, and FV, so the calculator finds ii numerically so that the TVM equation balances:

0=PV+PMT×1−(1+i)−Ni+FV(1+i)N0=PV+PMT×i1−(1+i)−N+(1+i)NFV

An iterative root‑finding algorithm (such as Newton–Raphson or bisection) adjusts ii until the left‑hand side is close to zero, which is the standard approach in financial calculators and spreadsheet functions.

6. Effective annual rate (EAR)

If your inputs involve compounding more than once per year, the effective annual rate (EAR) is:

EAR=(1+rm)m−1EAR=(1+mr)m−1

For continuous compounding:

EAR=er−1EAR=er−1

This explains why more frequent compounding leads to slightly higher growth than the nominal interest rate suggests.