Finance Calculator

Finance Calculator: How It Works

Time value of money is the idea that a unit of currency today is worth more than the same unit later, because today's can be put to work. Every loan, lease, bond, annuity and investment decision reduces to one equation with five variables — this calculator solves for whichever one you are missing.

The five variables

Symbol	Means	Sign convention
PV	Present value — the amount now	Negative if you pay it out
FV	Future value — the amount later	Positive if you receive it
PMT	Payment per period	Negative if you pay it
n	Number of periods	Always positive
r	Rate per period	As a decimal

The sign convention matters and is where most errors come from. Money flowing away from you is negative; money flowing toward you is positive. A loan is positive PV (you receive it) with negative PMT (you repay it). Getting the signs wrong produces answers that are right in magnitude and useless in meaning.

The core relationships

Single amount forward and back:

FV = PV × (1 + r)ⁿ · PV = FV ÷ (1 + r)ⁿ

A stream of equal payments:

FV_annuity = PMT × [((1 + r)ⁿ − 1) ÷ r]

PV_annuity = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

Discounting, and why it is the important half

Compounding — pushing money forward — feels natural. Discounting — pulling future money back to today — is the operation that actually settles arguments.

Promised in	Worth today at 8%	Worth today at 12%
1 year	92,590	89,290
5 years	68,060	56,740
10 years	46,320	32,200
20 years	21,450	10,370
30 years	9,940	3,340

Values shown for 100,000 received at each horizon. A promise of 100,000 in thirty years is worth about 10,000 today at 8% — and about 3,300 at 12%. This is why lottery annuity payouts and structured settlements are worth far less than their advertised totals, and why the discount rate chosen is the most consequential assumption in any valuation.

Ordinary annuity versus annuity due

An ordinary annuity pays at the end of each period — bonds, most loan repayments. An annuity due pays at the start — rent, leases, insurance premiums, most SIPs. An annuity due is worth (1 + r) times more, because every payment sits for one extra period. Over a long horizon that single factor is not trivial.

A worked comparison

You are offered 500,000 today or 60,000 a year for twelve years. At an 8% discount rate:

PV of the stream = 60,000 × [1 − 1.08⁻¹²] ÷ 0.08 = 452,140.

Take the lump sum. But the answer flips with the rate: at 5% the stream is worth 531,760, and taking it becomes the better choice. The correct discount rate is the return you could genuinely earn on the money — not a rate chosen to justify a preference.

Where it shows up in ordinary life

Deciding between a rebate now and lower payments later.
Valuing a pension option: lump sum against monthly income for life.
Comparing lease versus buy, once both are reduced to present value.
Judging whether an early-settlement discount on a debt is worth taking.
Assessing any 'no payments for 12 months' offer, which is simply a deferred cash flow.

Frequently Asked Questions

What discount rate should I use?

The return you could realistically earn on the money with comparable risk — your opportunity cost. For a safe cash flow, a deposit or government bond rate is appropriate. For a risky one, a higher rate. Using an unrealistically low rate makes future money look more valuable than it is.

Why does the sign convention matter?

The equation balances inflows against outflows. If everything is entered as positive, the relationship has no solution or produces a meaningless one. Money you pay out is negative; money you receive is positive.

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

Timing within the period. Ordinary annuities pay at the end, annuities due at the beginning. An annuity due is worth (1 + r) times more because each payment earns for one extra period.

Should I take a pension lump sum or monthly payments?

Compute the present value of the payment stream at a rate you could actually earn, then compare it against the lump sum. That gives you the financial answer — but longevity, tax treatment, inflation protection and whether the payments continue to a spouse all matter too, and none of them are in the arithmetic.

Does this handle uneven cash flows?

Not directly — it assumes equal periodic payments. For uneven flows, discount each one individually with PV = FV ÷ (1 + r)^n and add the results. That is exactly what a net present value calculation does.

Is inflation included?

Only if you use a real rate. If your discount rate is nominal, the answer is in nominal terms. Mixing a nominal rate with inflation-adjusted cash flows is a common and significant error.