BedrockCalc — bedrockcalc.com
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Finance Calculator
Five variables govern every time-value-of-money problem: N, I/Y, PV, PMT and FV. Enter any four and this finance calculator solves the fifth, shows the work, and shares the exact scenario with one link — a BA II Plus in your browser.
See how this works on one savings plan solved three ways — 3 real examples
Solving for future value (FV)
$0
Sum of payments
$0
Total interest
$0
Rate per period
0%
Total interest is signed: positive means interest earned, negative means interest paid.
Balance over the periods
The balance is the account value each period (opposite in sign to your PV/PMT inputs). It starts at −PV and ends at FV.
Period-by-period scheduleHow the balance builds each period
| Period | Start balance | Payment | Interest | End balance |
|---|
How this finance calculator solves for any TVM variable
Every time value of money problem is one equation linking the five variables. With the per-period rate r = (I/Y ÷ 100) ÷ P/Y and N periods, it is:
0 = PV + PMT · (1 − (1 + r)−N) / r · (1 + r·d) + FV · (1 + r)−N
d = 0 for end-of-period, 1 for beginning-of-period
Solving for PV, FV or PMT rearranges this directly. Solving for N uses a logarithm. Solving for I/Y has no closed form, so the engine brackets and root-finds the rate that makes the equation balance; when the cash flows never change sign no rate exists, and the calculator says so rather than inventing a number. Sum of payments is PMT × N and total interest is PV + PMT × N + FV in signed terms. The period-by-period schedule rolls the resolved cash flows forward at r per period (balanceₖ = balanceₖ₋₁ × (1 + r) − PMT), and its interest column sums to exactly the total interest above.
One assumption worth stating plainly: this solver compounds interest once per payment period, so payments-per-year and compounding-per-year are the same (P/Y = C/Y). That matches the default on most financial calculators. It does not model mismatched compounding, calendar dates or irregular cash flows.
Same equation, three unknowns
A $10,000 start plus $200 a month for ten years — solved once for the ending, once for the deposit, once for the rate.
What does this plan grow into?
future value$50,970
- A $10,000 start and $200 a month at 6% compound to $50,970 in ten years.
- Deposits account for $34,000 of it; the remaining $16,970 is interest doing the work.
- The rate matters twice — it grows the lump sum and every deposit along the way.
Four knowns — N, I/Y, PV and PMT — and the fifth number has no choice but to follow.
Load this example (opens in a new tab)What does $100,000 cost per month?
monthly deposit$610.21
- Reaching $100,000 in 120 months at 6% takes $610.21 a month, starting from nothing.
- The deposits sum to $73,225; growth contributes the other $26,775.
- Deposits made early have the most months to earn, which is how growth covers over a quarter of the goal.
The savings question runs backward: name the ending, and the equation prices the habit.
Load this example (opens in a new tab)What return does $50,000 require?
required annual return5.73%
- Turning the same $10,000-plus-$200 plan into $50,000 needs a 5.73% annual return.
- At 6% the plan lands on $50,970 instead, $970 past the target.
- Total interest along the way is exactly $16,000 — $50,000 minus the $34,000 deposited.
Solving for I/Y flips the question from what will this earn to what has to be earned.
Load this example (opens in a new tab)Illustrations only, not financial advice. Your own rate, taxes and insurance will differ — check with a qualified financial advisor before acting on any of this.
Time value of money, without the black box
- Four in, one out. Every present-value / future-value question is the same equation. Know any four of N, I/Y, PV, PMT and FV, and the fifth is fixed — this TVM calculator just does the rearranging.
- Signs carry the direction. Cash out is negative, cash in is positive. Get the signs right and loans, savings goals and annuities all use one tool; get them wrong and the answer flips.
- It works for loans and savings alike. A loan is PV positive (cash you get) with negative payments; a savings plan is negative PV and PMT building to a positive FV. Same math, opposite signs.
- Timing nudges the result. Beginning-of-period payments (annuity due) earn one extra period of interest versus end-of-period — small on short horizons, meaningful over decades.
- The schedule is the receipt. Every solved answer comes with a period-by-period balance you can export, so you can see present value become future value one step at a time.
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Frequently asked questions
What is the time value of money?
The time value of money is the idea that a dollar today is worth more than a dollar in the future, because money you hold now can earn interest. This finance calculator uses that principle to convert between present value, future value and a stream of payments — the same TVM math built into a BA II Plus or HP 12C financial calculator.
Which variable can this TVM calculator solve for?
Any one of the five: N (number of periods), I/Y (annual interest rate), PV (present value), PMT (the periodic payment) or FV (future value). Pick the one you want in the “Solve for” selector, fill in the other four, and the answer appears instantly — no keystroke sequence to memorize.
Why do some values need a negative sign?
A time-value-of-money equation only balances when cash flowing out and cash flowing in have opposite signs. The convention (the same one Excel and financial calculators use) is that money leaving your pocket is negative and money coming back to you is positive. If you invest $10,000 today, enter PV as −10,000; the future value it grows to comes back positive.
What do payments per year and payment timing change?
Payments per year (P/Y) sets how often a payment happens and how often interest compounds — 12 for monthly, 4 for quarterly, 1 for annual. The per-period rate is the annual I/Y divided by P/Y. Payment timing chooses an ordinary annuity (end of period) or an annuity due (beginning of period); beginning-of-period payments earn one extra period of interest, so they finish slightly ahead.
How does the calculator solve for the interest rate or N?
Solving for present value, future value or payment is a direct formula. Solving for the rate (I/Y) has no closed form, so the engine uses a numerical root-finder; solving for N uses a logarithm. If the cash flows all point the same direction — for example every value is negative — no rate can balance them, and the calculator tells you so instead of showing a meaningless number.
How is total interest calculated?
Total interest is the sum of every payment and the present and future values in signed terms: PV + PMT × N + FV. A positive result is interest you earned; a negative result is interest you paid. It equals the difference between the ending balance and everything you contributed, and the period-by-period schedule below adds up to exactly this figure.
Disclaimer: these calculators are educational tools, not financial advice. They model your inputs with published formulas, but they cannot know your full situation — for decisions with real stakes, talk to a qualified professional. Formulas and defaults last reviewed .