How to use this finance calculator
- Pick what to solve for: future value, payment, interest rate, number of periods or present value. That field disappears from the form.
- Enter the other four values. N is the total number of periods (10 years of monthly payments = 120) and I/Y is the annual interest rate.
- Use signs for direction: money you pay out is negative, money you receive is positive. Leave an amount at 0 if there is none.
- Open “Payments per year, compounding & timing” if you pay other than monthly, if interest compounds on a different schedule, or if payments come at the start of each period.
- Read the answer and the schedule, then switch the unknown to check the problem from another angle: a solved amount or rate carries over to its field.
What is the time value of money?
The time value of money is the idea that a dollar today is worth more than a dollar in the future, because money you have now can earn interest. Growth comes from compound interest, which Investor.gov defines as interest paid on principal and on accumulated interest. At 6% compounded monthly, $10,000 left alone grows to $18,193.97 in 10 years; run backward, $18,193.97 due in 10 years is worth $10,000 today. Every loan, savings plan and annuity is priced with this same idea.
The five TVM variables
- N — the number of periods (usually the number of payments). Years × payments per year.
- I/Y — the nominal annual interest rate, in percent. The calculator converts it to a rate per period.
- PV — present value: the amount at the start (a deposit, a loan balance, the price of an investment).
- PMT — the equal payment made or received every period. Use 0 for a single lump sum.
- FV — future value: the amount at the end (a savings goal, a remaining balance, a balloon payment).
Two settings complete the problem: P/Y, payments per year, and C/Y, compounding periods per year (normally the same as P/Y). A third, payment timing, says whether payments come at the end or the beginning of each period.
The TVM formula
All five variables are tied together by one equation. With payments at the end of each period (k = 0) or the beginning (k = 1):
PV × (1 + i)^N + PMT × (1 + i·k) × ((1 + i)^N − 1) / i + FV = 0
- i
- interest rate per period (see below)
- N
- number of periods
- PV, PMT, FV
- present value, payment and future value, signed as cash flows
- k
- 0 for end-of-period payments, 1 for beginning-of-period payments
The rate per period comes from the annual rate and the two frequencies. When C/Y equals P/Y it is simply I/Y ÷ P/Y:
i = (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1
FV, PV and PMT can be isolated algebraically, and N with logarithms. I/Y generally has no closed-form solution, so it is found by iteration, as spreadsheets do.
Worked example
Take the calculator’s default: PV = -$10,000.00, PMT = -$200.00, N = 120, I/Y = 6%, monthly payments and compounding. The rate per month is i = 6% ÷ 12 = 0.005, and (1 + i)N = 1.819397. The deposit grows to $10,000 × 1.819397 = $18,193.97, and the monthly payments grow to $200 × (1.819397 − 1) ÷ 0.005 = $32,775.87. Together that is FV = $50,969.84, of which $16,969.84 is interest on the $34,000 you put in.
The cash-flow sign convention (why answers can be negative)
TVM problems track money from your point of view: money you pay out is negative and money you receive is positive. Excel’s FV, PV, PMT, NPER and RATE functions use the same rule. A problem needs at least one outflow and one inflow; if every amount has the same sign, there is no rate or number of periods that balances the equation. Typical patterns:
| Situation | PV | PMT | FV |
|---|---|---|---|
| Saving toward a goal | − (initial deposit) | − (deposits) | + (balance you collect) |
| Taking out a loan or mortgage | + (loan you receive) | − (payments) | 0 (paid off) or − (balloon) |
| Living off a lump sum | − (amount you invest) | + (withdrawals) | 0 (used up) or + (what’s left) |
| Buying a bond | − (price you pay) | + (coupons) | + (face value at maturity) |
The schedule and chart show balances from your side as well: a savings balance is positive (the bank owes you), a loan balance is negative (you owe the lender), and the final balance equals FV (when N is fractional, it can pass FV slightly in the last period).
Three worked examples
1. Savings goal: how much to save each month
You want $50,000 for a down payment in 5 years, have $5,000 saved and assume a 4% return compounded monthly. Solve for PMT with N = 60, I/Y = 4, PV = -$5,000 (money you set aside) and FV = $50,000 (money you will collect). The answer, PMT = -$662.08, is negative because you pay it in every month. Your $44,724.61 of deposits earn $5,275.39 of interest.
2. Loan payment: a car loan
You borrow $35,000 for 60 months at 6.35%, the average new-car loan rate reported by Experian as of June 2026. The loan is money you receive, so PV = +35,000 and FV = 0 (paid off). Solving for PMT gives -$682.36 a month. Over the loan you repay $40,941.53, so interest costs $5,941.53. Use the interest rate on your loan contract here, not the APR, which also folds in fees. Our auto loan calculator adds taxes, trade-ins and fees.
3. Retirement lump sum: how much you need to retire
You want to withdraw $4,000 at the start of each month for 25 years from savings that earn 5%, spending the balance down to zero. Enter N = 300, I/Y = 5, PMT = +4,000 (money you receive), FV = 0, and set payments to the beginning of each period. Solving for PV gives -$687,091.19: negative, because that is what you must put in at retirement. Your withdrawals total $1,200,000.00, and $512,908.81 of that is interest earned along the way. For income plans with Social Security and inflation, try our retirement calculator.
Ordinary annuity vs. annuity due
An ordinary annuity has payments at the end of each period (most loans, most savings plans). An annuity due has them at the beginning (rent, leases, insurance premiums, withdrawals taken up front). Each annuity-due payment gets one more period of interest, so the payment stream is worth (1 + i) times as much.
- Default savings plan: FV is $50,969.84 with end-of-month deposits and $51,133.72 with beginning-of-month deposits.
- Retirement example: withdrawing at the start of each month requires $687,091.19; withdrawing at the end requires $684,240.19, because each withdrawal waits a month.
How to calculate TVM in Excel or Google Sheets
Excel and Google Sheets have one function per variable with the same argument order: =FV(rate, nper, pmt, pv, type), =PV(rate, nper, pmt, fv, type), =PMT(rate, nper, pv, fv, type), =NPER(rate, pmt, pv, fv, type) and =RATE(nper, pmt, pv, fv, type, guess). Enter the rate per period (6%/12 for monthly) and type = 1 for beginning-of-period payments. With the default deposits:
| What you want | Formula | Result |
|---|---|---|
| Future value (FV) | =FV(6%/12, 120, -200, -10000) | $50,969.84 |
| Payment to reach $60,000 (PMT) | =PMT(6%/12, 120, -10000, 60000) | -$255.10 |
| Rate to reach $60,000 (I/Y) | =RATE(120, -200, -10000, 60000)*12 | 8.283% |
| Months to reach $100,000 (N) | =NPER(6%/12, -200, -10000, 100000) | 206.44 |
| Lump sum needed today for $60,000 (PV) | =PV(6%/12, 120, -200, 60000) | -$14,963.27 |
RATE returns the rate per period, which is why the formula above multiplies by 12. If compounding differs from the payment frequency, compute the rate per period first, for example =(1+6%/2)^(2/12)-1 for 6% compounded semiannually with monthly payments (0.4939%).
How much $100 a month grows to
Future value of saving $100 at the end of every month, compounded monthly, starting from $0:
| Years | 2% | 4% | 6% | 8% | 10% |
|---|---|---|---|---|---|
| 5 years | $6,305 | $6,630 | $6,977 | $7,348 | $7,744 |
| 10 years | $13,272 | $14,725 | $16,388 | $18,295 | $20,484 |
| 15 years | $20,971 | $24,609 | $29,082 | $34,604 | $41,447 |
| 20 years | $29,480 | $36,677 | $46,204 | $58,902 | $75,937 |
| 25 years | $38,882 | $51,413 | $69,299 | $95,103 | $132,683 |
| 30 years | $49,273 | $69,405 | $100,452 | $149,036 | $226,049 |
| 40 years | $73,444 | $118,196 | $199,149 | $349,101 | $632,408 |
How much to save a month to reach $1 million
Monthly deposit needed to reach $1,000,000 from $0, with end-of-month deposits and monthly compounding. Returns are assumptions, not guarantees; see our investment calculator for more scenarios.
| Years | 4% | 6% | 8% | 10% |
|---|---|---|---|---|
| 10 years | $6,791 | $6,102 | $5,466 | $4,882 |
| 20 years | $2,726 | $2,164 | $1,698 | $1,317 |
| 30 years | $1,441 | $996 | $671 | $442 |
| 40 years | $846 | $502 | $286 | $158 |
Common TVM mistakes
- Mixing units. With monthly payments, N is in months and the rate per period is monthly. The calculator handles this through P/Y; in a spreadsheet, divide the rate and multiply the years yourself.
- All amounts positive. Deposits and loan payments are outflows (negative). Without opposite signs there is no solution.
- Wrong payment timing. Leaving payments at the beginning when they come at the end overstates growth and understates loan payments.
- Treating APY as I/Y. A 6% rate compounded monthly is an APY of 6.168%. If you only know the APY, set C/Y to 1.
- Using the APR for a payment. A loan’s APR includes fees, so the payment comes from the contract interest rate. See our loan calculator and interest rate calculator.
For growth with changing contributions, try the compound interest calculator.
Frequently asked questions
What does a finance calculator do?
A finance calculator solves time value of money problems: given any four of the five TVM variables (N, I/Y, PV, PMT and FV), it calculates the fifth. That covers savings goals, loan payments, investment growth and retirement income. For example, it shows that $10,000 plus $200 a month at 6% grows to $50,969.84 in 10 years, or that reaching $60,000 instead needs $255.10 a month.
Why is my answer negative?
A negative answer means money you pay out; a positive answer is money you receive. TVM math uses this cash-flow sign convention, and Microsoft documents the same rule for Excel’s financial functions. In the default example, PV (-$10,000.00) and PMT (-$200.00) are negative because you deposit them, and FV ($50,969.84) is positive because you collect it. If every amount has the same sign, no rate or number of periods can solve the problem.
What is the difference between P/Y and C/Y?
P/Y is the number of payments per year and C/Y is how many times a year interest compounds. They are usually equal (12 and 12 for monthly payments). When they differ, the rate per payment is (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1. For 6% compounded semiannually with monthly payments, that is 0.4939% a month instead of 0.5%.
How do I find the interest rate on a loan or investment?
Choose “Interest rate (I/Y)” as the unknown and enter N, PV, PMT and FV with the right signs. For example, borrowing $8,000 (PV = +8,000) and repaying $200 a month (PMT = −200) for 48 months works out to 9.24% a year. The calculator solves the TVM equation numerically, the same way Excel’s RATE function does.
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity payments happen at the end of each period; in an annuity due they happen at the beginning, so each payment earns (or costs) one extra period of interest. Saving $200 a month on top of $10,000 for 10 years at 6% gives $50,969.84 with end-of-month deposits and $51,133.72 with beginning-of-month deposits.
How do I do TVM calculations in Excel or Google Sheets?
Use the built-in functions FV, PV, PMT, NPER and RATE, which take the same arguments in the same order in Excel and Google Sheets. Enter the rate per period (annual rate ÷ 12 for monthly), the number of periods, and cash you pay out as negative numbers. For the default example, =FV(6%/12, 120, -200, -10000) returns $50,969.84. RATE returns a per-period rate, so multiply it by 12 for an annual rate.
Why is N not a whole number?
A fractional N means the target is reached partway through the last period. With $10,000 to start and $200 a month at 6%, reaching $100,000 takes N = 206.44 months: 206 full deposits, then one more month of interest alone carries the balance past $100,000. For a loan, a fractional N means a smaller last payment. The schedule shows exactly what happens in the final period.
Is I/Y the same as APY?
No. I/Y is a nominal annual rate: the stated rate before compounding. The annual percentage yield (APY) that banks must disclose reflects both the rate and how often interest compounds over a year. A 6% rate compounded monthly equals an APY of 6.168%. To enter an APY directly, set C/Y to 1 (annual compounding), which makes the effective annual rate equal I/Y.