TVM Calculator
Solve any one of the five time value of money keys, N, I/Y, PV, PMT or FV, the way a financial calculator does.
Result
Future value (FV): $10,511.40
A constant rate and level payments, one per period. Uneven cash flows need the NPV or IRR calculator.
- Present value (PV)
- $10,000.00
- Payment (PMT)
- $0.00
- Number of periods (N)
- 10
- Annual interest rate (I/Y)
- 6%
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Results are arithmetic on the returns, rates and horizons you enter, not a forecast and not investment, tax or retirement advice. The site supplies no expected return, inflation rate, contribution limit, tax rate or withdrawal rate. Real returns vary from year to year, and fees, taxes and the order of returns all change the outcome. Check anything that matters with a qualified adviser. Read the full disclaimer
How to use the TVM Calculator
- Choose the key to solve for, and who pays what, which sets the signs a financial calculator would need.
- Enter the other four keys as positive amounts, and how many periods fall in a year.
- Choose whether payments fall at the end of each period or the start, and read the answer.
The equation
Every time value of money problem with level payments is one equation in five quantities:
PV × (1 + i)^N + PMT × c × ((1 + i)^N − 1) ÷ i + FV = 0i = I/Y ÷ P/Y, c = 1 + i for payments at the start, 1 at the endMoney received counts as positive and money paid as negative. Given any four keys, the fifth follows. FV, PV and PMT rearrange directly. N comes from a logarithm. I/Y has no rearrangement, so the page searches for it, halving the gap until it is exact far beyond the digits shown.
Choosing who pays what
- Saving: you pay in the present value and each payment, and receive the future value.
- Borrowing: you receive the present value, then pay each payment and whatever is still owed at the end, which is the future value. Set FV to zero for a loan that is fully repaid.
- Drawing down: you pay in the present value and receive each payment, with the future value left over at the end.
A solved amount below zero means the money flows the other way from the pattern chosen: a borrowing FV below zero, for example, means the payments more than repay the loan.
Where the other pages fit
The future value, present value and annuity calculators each answer one of these questions with more explanation. The interest rate calculator solves I/Y for a loan with nothing left owing. Uneven cash flows, where the payment changes, need the NPV or IRR calculator.
With your numbers
- Rate per period i = 4% ÷ 1 = 4%
- PV × (1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i = FV
- N = 5, PV = $0.00, PMT = $3,000.00, FV = $16,248.97, I/Y = 4%
Quick reference
A constant rate and level payments, one per period. Uneven cash flows need the NPV or IRR calculator.
| Example | Result |
|---|---|
| FV of 3,000 a year for 5 years at 4% | Future value (FV): $16,248.97 |
| The same paid at the start of each year | Future value (FV): $16,898.93 |
| PV of 25,000 a year for 5 years at 8% | Present value (PV): $99,817.75 |
| PMT on 32,000 over 36 months at 6% | Payment (PMT): $973.50 |
| N for 100 to grow to 133.82 at 5% | Number of periods (N): 5.97 |
| I/Y for 1,000 to grow to 1,125.51 in 4 years | Annual interest rate (I/Y): 3% |
| Balance left on 200,000 at 6% after 60 payments of 1,500 | Future value (FV): €165,114.98 |
Common questions about the TVM Calculator
- How does this match the BA II Plus or an HP 12C?
- It solves the same equation with the same five keys. A financial calculator needs money you pay in entered as a negative number and money you receive as positive. Here you choose the pattern instead, saving, borrowing or drawing down, and type every amount as positive. The worked examples in OpenStax Principles of Finance come out the same, such as 3,000 a year for 5 years at 4% growing to 16,248.97.
- What does P/Y mean?
- Payments per year. I/Y is an annual rate, and it is divided by P/Y to get the rate for each period. Here payments and compounding happen equally often, which is the calculator default. N counts periods, not years: 30 years of monthly payments is N = 360.
- When should I use payments at the start?
- When each payment falls on the first day of its period, like rent or a lease, rather than the last day, like most loan payments. It is called an annuity due, or BGN mode, and each payment earns one more period of interest.
- Why does solving for I/Y or N sometimes give no answer?
- Because no rate, or no number of periods, makes the amounts balance. A loan payment smaller than the interest each period never repays the loan, so no N exists. The page then leaves the answer blank and says why, rather than showing a number that would be wrong.