💰 General Finance & Future Value Calculator
Project future capital accumulation based on lump sum savings, periodic deposits, and compound yield.
Time value of money: five variables, solve for any one
Nearly every question in finance reduces to the same relationship between five quantities: present value, future value, interest rate, number of periods and payment. Fix four and the fifth is determined. A mortgage, a savings plan, a bond price and a lease are all the same equation read from different angles.
PV × (1+r)n + PMT × [ ((1+r)n − 1) / r ] + FV = 0
The sign convention is what trips people up: money coming towards you is positive, money leaving you is negative. A loan has a positive present value and negative payments; a savings plan has negative payments and a positive future value.
The five questions
| Solve for | The question it answers | Typical use |
|---|---|---|
| Future value | What will this be worth? | Savings plan, investment projection |
| Present value | What is that future sum worth today? | Valuing a payout, comparing offers |
| Payment | What must I pay or save each period? | Loan instalment, savings target |
| Rate | What return or cost is implied? | Finding the real cost of finance |
| Periods | How long will it take? | Payoff date, time to a goal |
Present value, and why a dollar later is worth less
Money available now can be put to work, so a sum promised in the future is worth less than the same sum today. Discounting is just compounding run backwards:
PV = FV / (1 + r)n
$50,000 promised in ten years, discounted at 6%, is worth $27,920 today. At 3% it is worth $37,205. The discount rate is doing all the work, which is why arguments about valuation are usually arguments about the rate rather than about the cash flows.
Lump sum or instalments
A classic use. You are offered $200,000 now or $25,000 a year for ten years, a nominal total of $250,000. Discount the instalments at a rate you could realistically earn:
| Discount rate | Present value | Better choice |
|---|---|---|
| 3% | $213,255 | Instalments |
| 4.5% | $197,827 | Lump sum |
| 6% | $184,002 | Lump sum |
| 8% | $167,745 | Lump sum |
The crossover sits a little under 4.3%. If you can reliably earn more than that, take the lump sum; if not, the instalments are worth more. Tax treatment and the risk that the payer defaults both belong in the decision too.
Ordinary annuity versus annuity due
If payments land at the end of each period it is an ordinary annuity, which is the default for loans and most savings. If they land at the beginning, it is an annuity due, which is how rent and many leases work. Each payment then has one extra period to compound, so the value is higher by a factor of (1 + r). On a ten-year stream at 6% that is a 6% difference, which is not a rounding error.
A worked example
You want $60,000 in eight years for a deposit. You have $12,000 now and expect 5% a year. The existing $12,000 grows to $17,729, leaving $42,271 to be funded by contributions. Solving for the payment gives $360.82 a month. If the horizon were six years instead of eight, the required contribution rises to $561.35, because there are fewer periods for both the contributions and the growth.
Frequently Asked Questions (FAQs)
What discount rate should I use?
The return you could realistically get on the money with comparable risk. For a safe, near-certain cash flow, use a government bond yield. For a business project, use the firm's cost of capital. Using an optimistic rate makes future money look cheap and present money look expensive, which biases every decision that follows.
Why are my payments negative in the formula?
It is a sign convention, not an error. Cash leaving you is negative and cash arriving is positive, which is what makes the equation balance to zero. The calculator handles it for you; it matters if you are reproducing the result in a spreadsheet with PV or FV functions.
What is the difference between this and the compound interest calculator?
The compound interest calculator always solves for the final balance. This one lets you fix any four variables and solve for the fifth, including the rate and the number of periods, which is what you need when you are evaluating an offer rather than projecting a plan.
How do I handle irregular payments?
This calculator assumes equal payments at regular intervals. For uneven cash flows you need a net present value or internal rate of return calculation, which discounts each payment individually. A spreadsheet's NPV and IRR functions handle it.
Is the internal rate of return the same as the interest rate here?
For a simple stream of equal payments, yes: solving for the rate gives the IRR. They diverge for irregular cash flows, and IRR can produce multiple mathematical answers when cash flows change sign more than once.
Can I use this for bond pricing?
Yes. A bond is a present value calculation: the coupon payments are the annuity, the face value is the future value, and the discount rate is the yield to maturity. Price moves inversely to yield, which falls straight out of the formula.