How to use the finance calculator
- Choose the value to solve for: FV, PMT, PV, N or I/Y. Its box disappears from the form.
- Enter N, the total number of payment periods (120 for ten years of monthly payments).
- Enter I/Y, the annual interest rate.
- Enter PV (the amount at the start), PMT (the amount paid or received each period) and FV (the amount at the end), using the signs below. Enter 0 for any that don't apply.
- Choose payments per year and whether payments come at the end (most loans and savings plans) or the beginning of each period (rent, leases, annuities due).
The sign convention, simply
Think of every amount from your own pocket's point of view. Money that leaves you is negative. Money that comes to you is positive. If you deposit $10,000 in an account, PV is −10,000; the balance you withdraw at the end is a positive FV. If you borrow $25,000, PV is +25,000 because the lender hands it to you, and your payments are negative. A problem with every value the same sign has no answer, because no rate turns money paid into more money paid.
The TVM formula
The equation says that, once interest is counted, everything you pay out and everything you receive balances to zero. FV, PV and PMT are rearranged directly. N comes from logarithms. I/Y has no direct formula, so the calculator searches every rate from −99% to +100% per period and narrows each match down; if more than one rate fits, it says so. Interest compounds once per payment period, which is how most financial calculators behave when P/Y and C/Y are equal.
Worked example
The defaults are a savings plan: deposit $10,000 now (PV = −10,000), add $200 at the end of every month (PMT = −200), at 6% a year for 120 months. What will you have?
- Rate per period: 6 ÷ 100 ÷ 12 = 0.005.
- Growth over 120 months: 1.005^120 = 1.819397.
- The $10,000 grows to 10,000 × 1.819397 = $18,193.97.
- The payments grow to 200 × (1.819397 − 1) ÷ 0.005 = 200 × 163.8793 = $32,775.87.
- FV = $18,193.97 + $32,775.87 = $50,969.84, positive because you collect it.
You paid in $10,000 + 120 × $200 = $34,000, so the interest earned is $16,969.84.
The same plan, solved for each value
| Solve for | Other values | Answer |
|---|---|---|
| FV | the example | $50,969.84 |
| PMT | FV = 100,000 | −$499.18 a month |
| PV | FV = 100,000 | −$36,948.58 today |
| N | FV = 100,000 | 206.44 months |
| I/Y | FV = 100,000, N = 120 | 15.07% a year |
Switching the default to payments at the beginning of each month raises FV to $51,133.72, because every deposit earns one extra month of interest.
Frequently asked questions
Why is my answer negative?
A negative result means money leaves you. If you solve for the payment on a loan with a positive PV, the payment comes back negative because you pay it. If you expected a positive number, check that the values you entered follow the same rule.
What does "No interest rate balances these values" mean?
No rate can balance values that all point the same way, such as a negative PV, negative payments and a negative FV: that would be paying in forever and never getting anything back. Recheck which amounts you pay and which you receive, so that at least one is negative and one is positive.
Can I use this for a loan?
Yes. For a $25,000 loan at 7% over 60 months, set PV = 25,000, FV = 0, N = 60, I/Y = 7 and solve for PMT: the answer is −$495.03, the monthly payment. The payment calculator does the same with a full schedule.
How is this different from the future value and present value calculators?
Those are simpler single-purpose tools with positive amounts only. The future value calculator adds separate compounding frequencies and a period-by-period table, and the present value calculator discounts a lump sum and a stream of payments to today.
Related calculators
- Future Value Calculator — What a sum today plus regular payments grows to, with any compounding and payments at the start or end.
- Present Value Calculator — What a future sum, or a stream of regular payments, is worth today at a given discount rate.
- Payment Calculator — Monthly payment for a loan with a fixed term, or how long a fixed monthly payment takes to clear it.
- Interest Rate Calculator — Find the annual interest rate hidden in a loan from the amount, the term and the monthly payment.
Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.