TVM: PV, FV, payment, rate & periods

Finance Calculator: What Are Your Cash Flows Worth?

The Finance Calculator solves the Time Value of Money (TVM) equation for any one missing variable: present value, future value, payment, interest rate, or number of periods. Separate P/Y and C/Y settings follow BA II Plus conventions; the period schedule shows interest each period. Use it for loans, savings runs, or finance-course TVM problems. Estimates only; not tax or financial advice.

By Jeff Beem

Updated June 9, 2026

Solve for

Time Value of Money (TVM): pick the unknown, enter the other four. Future value: what the stream is worth at period N.

TVM variables

N (periods) , payment periods

10.0 years at 1/yr (P/Y). Match N to how often PMT occurs, not C/Y alone.

I/Y (interest rate), Annual rate (%)

PV (present value), ($)Negative = outflow

PMT (payment), ($)Negative = outflow

FV (future value), ($)

Advanced

P/Y (payments per year)

C/Y (compounds per year)

P/Y sets how often PMT occurs; C/Y sets how interest accrues. On a BA II Plus, mixing these up is the mistake that survives the whole exam.

Payment timing

Inflation rate (%)

Inflation adjustment uses today's dollars on the FV readout (default 3%).

Future Value

-$9,455.36

Outflow (negative)

Sum of payments $20,000

Total interest $9,455

TVM formula

PV(1+i)ⁿ + PMT × [(1+i)ⁿ - 1] / i × (1 + i×type) + FV = 0

Period 1

$20,000.00

PMT

-$2,000.00

Interest

$1,200.00

-$19,200.00

Period 2

$19,200.00

PMT

-$2,000.00

Interest

$1,152.00

-$18,352.00

Period 3

$18,352.00

PMT

-$2,000.00

Interest

$1,101.12

-$17,453.12

Period 4

$17,453.12

PMT

-$2,000.00

Interest

$1,047.19

-$16,500.31

Period 5

$16,500.31

PMT

-$2,000.00

Interest

$990.02

-$15,490.33

Period 6

$15,490.33

PMT

-$2,000.00

Interest

$929.42

-$14,419.75

Period 7

$14,419.75

PMT

-$2,000.00

Interest

$865.18

-$13,284.93

Period 8

$13,284.93

PMT

-$2,000.00

Interest

$797.10

-$12,082.03

Period 9

$12,082.03

PMT

-$2,000.00

Interest

$724.92

-$10,806.95

Period 10

$10,806.95

PMT

-$2,000.00

Interest

$648.42

-$9,455.36

Period	PV	PMT	Interest	FV
1	$20,000.00	-$2,000.00	$1,200.00	-$19,200.00
2	$19,200.00	-$2,000.00	$1,152.00	-$18,352.00
3	$18,352.00	-$2,000.00	$1,101.12	-$17,453.12
4	$17,453.12	-$2,000.00	$1,047.19	-$16,500.31
5	$16,500.31	-$2,000.00	$990.02	-$15,490.33
6	$15,490.33	-$2,000.00	$929.42	-$14,419.75
7	$14,419.75	-$2,000.00	$865.18	-$13,284.93
8	$13,284.93	-$2,000.00	$797.10	-$12,082.03
9	$12,082.03	-$2,000.00	$724.92	-$10,806.95
10	$10,806.95	-$2,000.00	$648.42	-$9,455.36

Quick reference

Signs: money leaving you (payments, deposits) is negative; money to you (loan proceeds, withdrawals) is positive. Flip every input and the solver still works, but mixed signs are what you want.

P/Y vs C/Y: N counts payment periods. If you pay monthly but interest compounds quarterly, set P/Y = 12 and C/Y = 4. The periodic rate follows the BA II Plus rule, not a simple I/Y ÷ 12.

Nominal FV can look impressive on a 20-year run. The inflation line below the result is the one I'd use for retirement back-of-napkin math.

Reading your TVM result

Match P/Y to how often PMT occurs, and keep signs consistent. One wrong sign on PV or PMT is the fastest way to get a plausible-looking number that's off by thousands.

Reading your results

Example: $20k in, −$2,000/yr for 10 years at 6% → FV ≈ −$9,455

The form opens with PV = $20,000 (money received), PMT = −$2,000 (paid each year), N = 10, I/Y = 6%, P/Y and C/Y both annual. FV lands near −$9,455: you'd still owe about $9,455 after 10 payments. Total interest in the summary is about $9,455. Open the period schedule to see interest shrink as the balance falls.

P/Y and C/Y are separate

Monthly payments with quarterly compounding: P/Y = 12, C/Y = 4, N = 120 for a 10-year loan. The periodic rate is not simply 6% ÷ 12. That split is what separates homework answers from the BA II Plus settings screen.

Ordinary vs due timing

End (ordinary) matches most loans and bonds. Begin (due) matches rent and some insurance: each payment gets one extra period of growth. On a 30-year 7% run, due timing can add a few percent versus end timing.

Nominal vs real FV

When you solve FV, check the inflation-adjusted tile if the horizon is long. Nominal growth can look fine while purchasing power barely moves.

Finance Calculator: Time Value of Money Solver

Solve for PV, FV, PMT, I/Y, or N with BA II Plus-style P/Y and C/Y settings. Period schedule included. Runs locally in your browser.

What This Calculator Does

This finance calculator solves the standard Time Value of Money (TVM) equation for any one missing variable. Enter four of N, I/Y, PV, PMT, and FV; it returns the fifth, plus total interest, sum of payments, an optional inflation-adjusted FV, and a period-by-period schedule. P/Y (payments per year) and C/Y (compounding periods per year) can differ, matching textbook and BA II Plus behavior. It does not handle variable rates, taxes, or fees. For month-by-month mortgage detail with extra payments, use the amortization calculator.

How the Math Works

All five variables must satisfy the TVM balance equation (ordinary annuity shown; due multiplies the annuity factor by (1+i)):

0 = PV(1+i)^n + PMT \cdot \frac{(1+i)^n - 1}{i} \cdot (1+i)^{\,T} + FV

I/Y is the nominal annual rate. The periodic rate i per payment period is:

i = \left(1 + \frac{I/Y/100}{C/Y}\right)^{C/Y \div P/Y} - 1

When P/Y = C/Y = 12 and I/Y = 6%, i ≈ 0.005 per month. Worked example (defaults on the form): PV = $20,000, PMT = −$2,000, N = 10, I/Y = 6%, annual P/Y and C/Y. FV ≈ −$9,455.36; total interest ≈ $9,455.36. For I/Y, there is no closed form; the tool uses Newton-Raphson on i then converts back to nominal I/Y. If PV, PMT, and FV are all zero, any rate works and the result is undefined.

How to Use This Calculator

Pick the unknown at the top. Fill the other four fields with signed dollars (negative = out of your pocket). Set P/Y to match payment frequency and C/Y to match how interest accrues. N is always the total number of payments. End timing is ordinary; Begin is annuity due. Results update as you type. Scroll to the period schedule to audit interest each period. When solving FV, compare nominal and inflation-adjusted values for long horizons.

Loan payment example (solve for PMT)

$300,000 borrowed at 6.5% for 30 years, monthly: N = 360, I/Y = 6.5, P/Y = 12, C/Y = 12, PV = 300,000, FV = 0. PMT ≈ −$1,896 per month (negative because you pay). Total interest over the life is roughly $382,000 on top of principal. Run the same inputs here and trace the schedule if a lender quote differs by more than a few dollars.

Investment growth example (solve for FV)

$10,000 upfront plus $500/month for 20 years at 7%, monthly compounding: PV = −10,000, PMT = −500, N = 240, I/Y = 7, P/Y = 12, C/Y = 12. FV ≈ $301,000 nominal before inflation. Toggle the inflation field to see purchasing power in today's dollars. For a simpler growth-only UI, try the investment calculator.

Ordinary annuity vs annuity due

End-of-period payments (ordinary) fit most amortizing loans. Begin-of-period (due) fits rent and some insurance premiums: each payment earns one extra period at rate i. On a 30-year 7% loan-sized example, due timing can lift the outcome a few percent versus ordinary. Use the payment timing dropdown; the schedule recalculates immediately.

Finance Calculator FAQ

How do I use a Time Value of Money (TVM) calculator?

Tap the variable you want (N, I/Y, PV, PMT, or FV) and fill in the other four. Outflows are negative: loan payments, savings deposits. Inflows are positive: loan proceeds, withdrawals. The schedule table below the result shows how the balance moves period by period.

Why is my finance calculator result negative?

Negative usually means money out. A −$1,896 PMT on a mortgage is you paying each month. A −$9,455 FV on the default loan example means you still owe that much after 10 annual payments. Positive FV on an investment run is what you'd have left in the account.

What is the difference between P/Y and C/Y on a TVM calculator?

P/Y is how often payments happen; C/Y is how often interest compounds. They can differ. A loan with monthly payments and quarterly compounding needs P/Y = 12 and C/Y = 4. Set N to the total count of payments (120 for 10 years monthly), not calendar years alone.

How do I find the interest rate on a loan with a TVM solver?

Choose I/Y, enter N, PV (loan amount as positive), PMT (payment as negative), and FV (0 for paid-off). The solver iterates to the nominal annual rate. Dealer quotes that include fees may run higher than the nominal rate you get here.

What does N mean on a finance calculator?

N is the count of payment periods, not necessarily years. Ten years of monthly payments means N = 120 when P/Y = 12. The hint under the N field converts to years using your P/Y setting.

Should I use inflation-adjusted future value for retirement?

For anything 15+ years out, yes. At 3% inflation, $1M nominal in 20 years is roughly $550k in today's dollars. The inflation line on the FV result is a quick purchasing-power check, not a forecast of actual CPI.

Sources & citations

References used for the calculation method and definitions. Links open in a new tab when available.

[1]

SEC – Investor.gov: Compound Interest (Glossary)

SEC investor education glossary definition of compound interest, the growth mechanism behind TVM future-value calculations.

[2]

CFA Institute – Time Value of Money

CFA Institute refresher on present value, future value, annuities, and the relationship between nominal rates and payment periods.

Financial Estimation Note

General Projections: Results are mathematical estimates based on the rates and formulas currently loaded for this tool, including year-specific tax data where noted. They are intended for high-level planning only.

No Advice Provided: This site does not provide financial, tax, or legal advice. Using this tool does not create a client-advisor relationship with CalcRegistry.

Confirm Numbers: Financial laws change frequently. Please verify all results with a qualified professional (CPA, Financial Planner, or Lawyer) before making significant financial decisions.