About the Time Value of Money Calculator
This time value of money (TVM) calculator works like the TVM keys on a BA II Plus or HP 12C financial calculator. Pick the unknown — future value, present value, payment, number of periods or interest rate — enter the other four, and it solves the standard TVM equation instantly.
It is built for finance and accounting students checking homework and CFA, CFP or CPA exam practice, as well as anyone pricing a loan, annuity, savings plan or bond-like cash flow. It supports payments at the end (ordinary annuity) or beginning (annuity due) of each period and any compounding frequency from yearly to daily.
Use the cash-flow sign convention: money you pay out (a deposit, an investment, a loan payment) is negative and money you receive (a loan, a withdrawal, a maturity value) is positive. The interest rate is entered as an annual rate and divided by the periods per year, and N is the total number of periods, not years.
With the default inputs, the solved value is 50,969.8367. Change any value above to recalculate instantly.
How to use the time value of money calculator
- 1Choose which value to solve for.
- 2Enter the other values using signs: money paid out is negative, money received is positive.
- 3Enter the annual rate and choose how many periods there are per year.
- 4Set N as the total number of periods (years × periods per year).
- 5Pick end or beginning-of-period payments and read the solved value.
Formula and method
All five TVM variables are linked by one equation, where i is the periodic rate (annual rate ÷ periods per year) and t is 0 for end-of-period payments or 1 for beginning-of-period payments. Given any four, the fifth is found: FV, PV and PMT are solved algebraically, N with logarithms, and the interest rate numerically by bisection because it has no closed-form solution.
Cash flows follow the sign convention used by financial calculators: outflows are negative and inflows positive, so a valid problem needs at least one of each. When i is zero the equation reduces to PV + PMT × N + FV = 0. The effective annual rate is (1 + i)^P/Y − 1.
- PV
- Present value (cash flow now)
- PMT
- Level payment each period
- FV
- Future value (cash flow at the end)
- N
- Total number of periods
- i
- Periodic rate = I/Y ÷ P/Y
- t
- 0 = payments at end, 1 = payments at beginning
Worked examples
FV of $10,000 plus $200 a month for 10 years at 6%
Depositing $10,000 now (PV −10,000) and $200 at the end of each month (PMT −200) for 120 months at 6% compounded monthly grows to about $50,970. You paid in $34,000, so about $16,970 is interest.
Monthly payment on a $300,000, 30-year loan at 6.5%
Receiving $300,000 today (PV +300,000) and paying it off to zero over 360 months at 6.5% needs a payment of $1,896.20 a month (shown negative because you pay it). Total interest is about $382,633.
Rate needed to double money in 10 years
Investing $1,000 (PV −1,000) to receive $2,000 in 10 annual periods requires a 7.18% annual return — close to the Rule of 72 estimate of 7.2%.
Months to reach $20,000 at 5%
Starting with $5,000 and adding $100 a month at 5% compounded monthly, it takes about 100.3 months — just over 8 years and 4 months — to reach $20,000.
Present value of $100,000 in 18 years at 6%
To have $100,000 in 18 years at 6% a year with no further deposits, you would need to invest about $35,034 today (shown negative as an outflow).
Annuity due: same savings plan with deposits at the start of each month
Moving each $200 deposit to the start of the month gives every payment one extra month of interest, raising the future value from about $50,970 to about $51,134.
Frequently asked questions
What is the time value of money?+
It is the principle that a dollar today is worth more than a dollar in the future because today’s dollar can be invested to earn interest. TVM math converts cash flows at different dates to a common point in time so they can be compared.
Why are some values negative?+
Financial calculators use a cash-flow sign convention: money leaving your pocket is negative and money coming in is positive. A savings problem has a negative PV and PMT and a positive FV; a loan has a positive PV and negative PMT.
What is the difference between an ordinary annuity and an annuity due?+
In an ordinary annuity payments happen at the end of each period (most loans and savings plans). In an annuity due they happen at the start (rent, leases, many insurance premiums), so each payment earns one extra period of interest.
Is N years or periods?+
N is the total number of periods. For monthly payments over 30 years, N is 360 and periods per year is 12. For an annual problem over 10 years, N is 10 and periods per year is 1.
How is the interest rate solved?+
There is no algebraic formula for the rate, so the calculator searches numerically: it finds a rate range where the TVM equation changes sign and narrows it by bisection until the answer is accurate to many decimal places. Handheld financial calculators use a similar iterative search, so answers match to the displayed precision.