Present & Future Value Calculator (TVM Solver)
A financial calculator’s TVM keys in your browser: give any four values, get the fifth.
Schedule
How this was calculated
Results are estimates for general information and planning, not financial advice. Banks and institutions may calculate differently (rounding, fees, rate changes). Confirm figures with your lender or a qualified adviser before deciding.
About the Present & Future Value Calculator (TVM Solver)
Present value, future value, loan payments, savings targets and the rate of return all come from one equation linking five numbers: the number of payments N, the interest rate I/Y, the present value PV, the payment PMT and the future value FV. A financial calculator such as the Texas Instruments BA II Plus solves it for whichever one you leave out, and so does this page — with payments and compounding per year (P/Y and C/Y), and payments at the end (END) or the start (BGN) of each period.
Two more modes cover what the five keys do not: a growing annuity, whose payment rises by a fixed percentage each period (a salary-linked saving plan, an inflation-linked pension), and a perpetuity, level or growing, that never ends (a preference dividend, an endowment). Every answer comes with the formula, your numbers in it and a schedule you can download. Nothing you enter leaves your browser.
How to use it
- Choose TVM solver, Growing annuity or Perpetuity, and the currency.
- TVM solver: pick the value to find (N, I/Y, PV, PMT or FV) and enter the other four. Money you pay out is negative, money you receive positive — a loan you take is a positive PV with negative payments; a saving plan is negative deposits and a positive FV.
- Set payments a year (P/Y) and, if interest is compounded differently, compounding a year (C/Y). Choose End for payments at the end of each period (loans, most savings) or Start for payments in advance (rent, leases, an annuity due).
- Read the answer and the schedule. To check it, find another value: the answer stays in its field at full precision, so finding N back from the payment you just found gives exactly the N you started with.
- Copy the summary or download the schedule as CSV.
Examples
N = 360, I/Y = 6, PV = 2,00,000, FV = 0, P/Y = C/Y = 12, END
PMT = −1,199.10 a month; after the first 12 payments the balance is 1,97,543.98 and 11,933.19 has gone in interest
N = 120, I/Y = 8, PV = 0, PMT = −500, P/Y = C/Y = 12
FV = 91,473.02 with END · 92,082.84 with BGN (each deposit earns one more month)
N = 5, I/Y = 5, PMT = 0, FV = 1,000, P/Y = C/Y = 1
PV = −783.53: pay 783.53 today to receive 1,000 in five years at 5%
N = 10, PV = −10,000, PMT = 0, FV = 20,000, P/Y = C/Y = 1
I/Y = 7.1773% a year
I/Y = 8, PV = 0, PMT = −500, FV = 1,00,000, P/Y = C/Y = 12
N = 127.52 deposits: 127 of 500 and a smaller 128th (10.63 years)
First payment 10,000, growing 3% a year, 20 payments, 8% a year, P/Y = C/Y = 1, END
PV = 1,22,500.41 · FV = 5,70,969.18 · last payment 17,535.06
100 a year for ever at 5%; or 100 growing 3% a year at 8%
PV = 2,000 in both cases (100 ÷ 0.05 and 100 ÷ (0.08 − 0.03))
Common uses
- Work out a loan’s EMI or how long a prepayment shortens it, and see the amortization schedule.
- Find what a monthly saving grows to, the deposit a goal needs, or how long it takes.
- Value a pension, an annuity or a lease, with payments in advance or in arrears.
- Check homework and exam answers in finance courses that use a BA II Plus or HP 12C.
The TVM equation
With i the interest rate per payment period and k = 1 for payments at the start of each period (0 at the end):
PV + PMT × (1 + i·k) × (1 − (1 + i)^−N) ÷ i + FV × (1 + i)^−N = 0
- FV = −[PV × (1 + i)^N + PMT × (1 + i·k) × ((1 + i)^N − 1) ÷ i]
- PV = −[FV × (1 + i)^−N + PMT × (1 + i·k) × (1 − (1 + i)^−N) ÷ i]
- PMT = −[PV + FV × (1 + i)^−N] ÷ [(1 + i·k) × (1 − (1 + i)^−N) ÷ i]
- N = ln((PMT·(1 + i·k) ÷ i − FV) ÷ (PV + PMT·(1 + i·k) ÷ i)) ÷ ln(1 + i)
- I/Y has no formula; it is found by searching for the rate that makes the equation zero, as a calculator’s solver does. When more than one rate fits (unusual sign patterns), all are listed.
The equation and the sign convention are the ones taught in the CFA Institute’s Quantitative Methods readings and built into the TVM keys of the BA II Plus and HP 12C.
P/Y and C/Y: payments and compounding a year
I/Y is a nominal yearly rate. When interest is compounded as often as payments are made (C/Y = P/Y), the rate per payment is simply I/Y ÷ P/Y: 6% a year paid monthly is 0.5% a month. When they differ, the rate per payment period is
i = (1 + I/Y ÷ (100 × C/Y))^(C/Y ÷ P/Y) − 1
so 8% compounded quarterly with monthly payments is 0.66227% a month, an effective 8.2432% a year. On a BA II Plus, entering P/Y sets C/Y to the same value; here too C/Y follows P/Y until you change it.
END or BGN
- END (an ordinary annuity): each payment comes at the end of its period — loan EMIs, most savings plans, bond coupons.
- BGN (an annuity due): each payment comes at the start — rent, leases and insurance premiums paid in advance. Each payment then earns, or is charged, one more period of interest, so the present and future values of the payments are (1 + i) times larger.
Growing annuities and perpetuities
- Growing annuity: N payments, the first PMT₁, each (1 + g) times the one before:
PV = PMT₁ × (1 − ((1 + g) ÷ (1 + i))^N) ÷ (i − g), andPV = PMT₁ × N ÷ (1 + i)when i = g. Its FV is PV × (1 + i)^N. - Perpetuity: payments for ever,
PV = PMT ÷ i; growing at g,PV = PMT ÷ (i − g), which exists only when i > g. This is the Gordon growth formula used to value shares from their dividends. - With payments at the start, both values are multiplied by (1 + i).
Here the growth rate is per payment period: with yearly payments it is a yearly growth rate.
Limitations
- One interest rate applies for the whole term. For a rate that changes, split the problem: the FV of the first part becomes the PV of the next.
- Days are not counted: every payment period has the same length. For cash flows on irregular dates use the XIRR calculator.
- Taxes, fees and inflation are not included unless you put them in the amounts or the rate.
- N can be up to 10,000 payments; the schedule lists up to 1,200 rows one by one and longer ones year by year. A growing annuity has at most 1,200 payments.
Privacy
Everything is calculated in your browser. The values and schedules are never uploaded or stored on a server.
Frequently asked questions
Why do some values have to be negative?
The equation balances money going out against money coming in, so they need opposite signs — the convention of every financial calculator. If you borrow 2,00,000 (PV positive, you receive it), your payments are negative. If you save 500 a month (PMT negative), the amount you collect at the end is positive. All values with the same sign is an error: nothing could balance them.
What is the difference between present value and future value?
Present value is what a future amount or a series of payments is worth today, after discounting at the interest rate; future value is what money today, or a series of payments, grows to by a later date. 783.53 today and 1,000 in five years are the same money at 5% a year.
What is the difference between an annuity due and an ordinary annuity?
An ordinary annuity pays at the end of each period (END), an annuity due at the start (BGN). An annuity due is worth (1 + i) times as much, because every payment arrives one period earlier.
Why is N not a whole number?
Because no whole number of equal payments hits the target exactly. 127.52 monthly deposits of 500 at 8% reach 1,00,000: in practice that is 127 full deposits and a smaller last one, which the schedule shows.
How do I convert an EMI rate or a monthly rate?
Enter the yearly rate in I/Y with P/Y = 12. A lender’s “12% a year” on a monthly loan is 1% a month (C/Y = 12). If you know an effective yearly rate instead, set C/Y = 1: the monthly rate is then (1 + rate)^(1/12) − 1.
Is a perpetuity realistic?
Nothing pays for ever, but distant payments are worth so little today that a perpetuity is a good approximation for long-lived payments. At 5%, the first 50 years of a level perpetuity are already 91% of its value; the table shows the share for your numbers.