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Financial Calculator

A time-value-of-money keypad: enter any four of N, I/Y, PV, PMT and FV, press CPT and the fifth, with payments and compounding per year and BGN/END.

Level: Grade 11 to college

  • Common Core standard HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Printable worksheet

Financial Calculator

ENDP/Y 1 · C/Y 1

Display: 0

TVM registers

N
0
I/Y
0%
PV
0
PMT
0
FV
0
P/Y
1
C/Y
1
Timing
END

Sign convention: money you receive is positive and money you pay out is negative, so a loan is +PV and its payments are −PMT. P/Y and C/Y start at 1; set P/Y to 12 for monthly payments (C/Y follows it). These are generic financial-calculator conventions, not any one brand's.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

What this calculator does

Work out a loan payment, a savings goal, an interest rate or how long something takes, all on one keypad. A financial calculator solves time-value-of-money (TVM) problems, the math of how money grows with interest over time. It uses five keys. N is the number of payments and I/Y is the yearly interest rate. PV (present value) is the amount today, PMT is the payment each period and FV (future value) is the amount at the end. Enter any four, press CPT (compute) and then the fifth key. It works out the missing one. The same five keys handle loans, mortgages, savings plans, annuities (a series of equal payments) and investments.

This is a generic financial keypad, not a copy of any brand. It follows the common rules. Money you receive is positive, and money you pay out is negative. P/Y sets payments per year, and C/Y sets how many times a year interest compounds (is added). BGN and END say whether payments fall at the start or the end of each period. Every answer comes from the same tested solver as this site's loan, savings and annuity calculators.

Where it's used

Why this math matters outside the classroom:

  • Car loans. A buyer finds that $25,000 at 6.9% for 60 months costs $493.85 a month.
  • Mortgages. A home buyer finds the monthly principal and interest on a $320,000, 30-year loan at 6.5% is $2,022.62.
  • Retirement saving. A saver finds that $500 a month for 20 years at 6% grows to about $231,020.45.
  • Finance courses. Business students check textbook TVM problems, such as the rate that doubles money in 10 years, about 7.18%.
  • Savings goals. A family works out the monthly deposit, about $450, to turn $2,500 into $20,000 in 3 years at 4%.

Grade level and standards: Grade 11 to college; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Press CLR TVM to clear the five stored values (registers). Then set the payments per year. For monthly payments, type 12 and press P/Y (C/Y is set to match).
  2. Type each known value and press its key: 60 N, 6.9 I/Y, 25000 PV, 0 FV. Use ± for money you pay out, such as a deposit.
  3. Press CPT, then the key you want. For example, CPT PMT gives the payment. A negative answer is money paid out.
  4. Use BGN for payments at the start of each period, like rent or an annuity due. Use END, the default, for loans and most savings.

What the inputs mean

Solve for
The value to work out. On the keypad, you do the same by pressing CPT and then that key.
PV (present value)
Positive if you receive it, like a loan you take out. Negative if you pay it, like a deposit or the price of an investment.
PMT (payment each period)
The same sign rule. Loan payments and regular deposits are negative.
P/Y (payments per year)
Payments per year: 12 for monthly, 1 for yearly. The keypad starts at 1, and then I/Y is the rate per period.
C/Y (compounding periods per year)
How many times a year interest compounds. It's usually the same as P/Y. A Canadian mortgage, for example, is P/Y 12 and C/Y 2.

Formula and method

i = I/Y ÷ 100 ÷ C/Y when C/Y = P/Y, otherwise i = (1 + I/Y ÷ 100 ÷ C/Y)^(C/Y ÷ P/Y) − 1
PV × (1 + i)^N + PMT × (1 + i × k) × ((1 + i)^N − 1) ÷ i + FV = 0
k = 0 for END (payments at the end of each period), k = 1 for BGN
With i = 0: PV + PMT × N + FV = 0

In the formulas, i is the interest rate for one payment period, as a decimal. N, PV, PMT and FV are the keys described above, and C/Y and P/Y are the compounding periods and payments per year. k is 0 or 1 depending on when payments are made.

One equation ties all five keys together. Grow today's amount (PV) for N periods. Add every payment, grown to the end. Add the future value. The total comes to zero. That only works with signs: money coming in is positive and money going out is negative. So a loan (+PV) is balanced by your payments (−PMT).

N, PV, PMT and FV are found by rearranging the equation. The interest rate can't be pulled out on its own, so I/Y is found by trial. The solver tries possible rates to find one that balances the equation. Then it zeroes in on the exact rate with a standard search technique called Brent's method.

Worked example

A $25,000 car loan at 6.9% APR, repaid monthly over 60 months. What is the payment?

  1. Press CLR TVM, then 12 P/Y for monthly payments (C/Y becomes 12 too) and keep END.
  2. 60 N, 6.9 I/Y, 25000 PV (you receive the money, so it is positive), 0 FV (the loan is paid off).
  3. The rate per month is i = 6.9 ÷ 100 ÷ 12 = 0.00575.
  4. CPT PMT: −25000 × 0.00575 ÷ (1 − 1.00575^(−60)) ≈ −493.85.

Result: The payment is −$493.85 a month. It's negative because it's money you pay out. Over 60 months, that's −$29,631.08 in all.

Understanding the result

The sign of an answer is part of the answer. CPT PMT = −493.85 means you pay $493.85 each period. If you get an error for I/Y or N, check the signs. PV, PMT and FV can't all be positive, because then money only ever flows one way.

N doesn't have to be a whole number. CPT N = 59.6 means 59 full payments and a smaller final one.

Assumptions and limitations

  • Payments are equal and evenly spaced, and the interest rate stays the same for the whole term.
  • Interest compounds C/Y times a year. That's converted to an equal rate for each payment period.
  • P/Y and C/Y start at 1. Setting P/Y also sets C/Y to the same value.
  • This keypad does time value of money only. It has no worksheets for payment schedules (amortization), cash flows (NPV/IRR), bonds or depreciation.
  • Real calculators differ in key names, starting settings and how they clear. The keys here are generic.
  • Results are rounded on screen to 12 significant digits. Lenders round payments to the cent and may adjust the last one.

Frequently asked questions

Why is my payment negative?

Because of the sign rule. Money coming to you (the loan) is positive, and money leaving you (each payment) is negative. That's what lets the equation balance. −493.85 means you pay $493.85.

What do P/Y and C/Y do?

P/Y is how many payments there are in a year. C/Y is how many times interest compounds in a year. With P/Y = 12, you enter N in months and I/Y as the yearly rate, and the calculator works out the monthly rate. Forgetting to set P/Y is the most common reason for a wrong answer, so it's worth a quick check.

When should I use BGN?

Use it when each payment is made at the start of the period. Examples are rent, leases, and savings deposited at the start of each month (an annuity due). Loans and most savings plans pay at the end of each period, which is END.

Why do I get an error when computing I/Y?

Usually it's the signs. For a rate to exist, money has to flow both ways. For example, PV = −1,000 (you invest) and FV = +2,000 (you get it back). If both are positive, no rate can balance the equation.

How this calculator is checked

Method: The standard time-value-of-money equation for level payments with compound interest; I/Y found by a bracketing scan and Brent's method. Checked against textbook examples and the site's loan, mortgage, savings and annuity calculators. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-19. Found a problem? Tell us.

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