— Investment
Time Value of Money Calculator
The classic five-variable solver — number of periods, interest rate, present value, payment and future value. Enter any four and it works out the fifth.
Future value (FV)
$37,405.09
- Sum of payments
- $-12,000
- Effective annual rate
- 7.23%
— Year by year
| Year | Payments | Interest | Balance |
|---|---|---|---|
| 1 | $1,200 | $762.16 | $11,962.16 |
| 2 | $1,200 | $904 | $14,066.16 |
| 3 | $1,200 | $1,056.1 | $16,322.27 |
| 4 | $1,200 | $1,219.2 | $18,741.46 |
| 5 | $1,200 | $1,394.08 | $21,335.54 |
| 6 | $1,200 | $1,581.61 | $24,117.15 |
| 7 | $1,200 | $1,782.69 | $27,099.84 |
| 8 | $1,200 | $1,998.31 | $30,298.15 |
| 9 | $1,200 | $2,229.51 | $33,727.66 |
| 10 | $1,200 | $2,477.43 | $37,405.09 |
— Value over time
Download— How it works
PV·(1 + i)^N + PMT · [((1 + i)^N − 1) ÷ i]·(1 + i·type) + FV = 0
The five variables
Every time-value-of-money problem links five quantities: the number of periods (N), the interest rate per year (I/Y), the present value (PV), the payment each period (PMT) and the future value (FV). Fix any four and the fifth is determined. This is the engine behind a financial calculator — and behind loans, savings, annuities and bond pricing alike.
Pick what to solve for at the top and that field disappears, because it becomes the answer. The remaining four are yours to set.
Worked example — invest $10,000 now plus $100 a month for 10 years at 7%, solving for FV: PV = −10,000, PMT = −100, N = 120, I/Y = 7%, P/Y = 12. The solver returns FV ≈ $37,405 — the positive amount you would receive at the end.
The sign convention
TVM uses signs to tell cash in from cash out. Money you pay out — a deposit, an investment, a loan repayment — is negative; money you receive is positive. That is why the example above enters the deposit and payments as negatives and gets a positive future value back.
The rule keeps every scenario consistent. For a loan, the amount borrowed (PV) is positive (you receive it) and the repayments (PMT) are negative; for savings, the deposits are negative and the final balance is positive. If a result looks backwards, it is almost always a sign that needs flipping.
Solving for rate or N
Future value, present value and payment each have a direct formula — rearrange the TVM equation and read off the answer. The interest rate and the number of periods do not: there is no closed form once payments are involved, so the calculator solves them numerically, narrowing the range until the equation balances.
The chart traces the account balance over time for the solved scenario — rising as a saving builds, or falling as a loan is paid down — so you can see the path, not just the endpoints. The yearly table lists the same balance with the payments and interest each year.
— Reader questions
Why are some values negative?
TVM uses the cash-flow sign convention: money leaving you (deposits, investments, loan repayments) is negative, money coming to you is positive. Mixing the signs correctly is what lets one formula handle both loans and investments. If your answer has the wrong sign, flip the sign of an input.
How is this different from the other interest calculators?
It is the general solver they are all special cases of. The Compound Interest and Future Value calculators only compute FV; this one solves for any of the five variables and uses the signed convention, so it also handles loans and bond-style problems. It is the financial-calculator tool, kept deliberately general.
What does “periods per year” do?
It sets how often interest is applied and payments are made. N is the total number of periods, and the annual rate is divided across them — so 120 periods at 12 per year is 10 years compounding monthly.
What is the difference between end and start of period?
Payments at the end of each period (an ordinary annuity) earn no interest in the period they are made; payments at the start (an annuity due) earn one extra period of interest. Rent and many savings deposits are start-of-period; loan payments are usually end-of-period.
Can it solve for the interest rate?
Yes. Choose “Rate” and the calculator finds the annual rate that makes the other four values consistent — the same idea as an internal rate of return for a single fixed payment stream.