This finance calculator can be used to calculate the future value (FV), periodic payment (PMT), interest rate (I/Y), number of compounding periods (N), and PV (Present Value). Each of the following tabs represents the parameters to be calculated. It works the same way as the 5-key time value of money calculators, such as BA II Plus or HP 12CP calculator.
Modify the values and click the calculate button to use
This finance calculator handles both lump-sum and annuity problems. Enter any four of the five standard TVM variables — N (number of compounding periods), I/Y (annual interest rate), PV (present value), PMT (periodic payment), and FV (future value) — and it instantly solves for the missing one. You can set the compounding frequency (monthly, quarterly, annually) and specify whether payments occur at the beginning or end of each period (ordinary annuity vs. annuity due). A brief step-by-step solution display shows you the formula being applied, so the result isn't just a number — you understand why it came out that way. Whether you're a student working through a finance textbook problem or a homeowner deciding whether to refinance, this tool does the heavy lifting.
1. Identify which variable you want to solve for (PV, FV, PMT, I/Y, or N) and leave that field blank.
2. Enter the known values in the remaining four fields: N (periods), I/Y (rate per year), PV (present value), PMT (periodic payment), FV (future value).
3. Set the compounding frequency — monthly is most common for loans and savings.
4. Indicate whether payments are made at the end of each period (ordinary annuity, the default) or the beginning (annuity due).
5. Click "Calculate" to solve for the missing variable.
6. Review the step-by-step breakdown displayed below the result to verify the logic.
Core TVM Formula (lump sum, no payment): FV = PV × (1 + r)^n, or rearranged: PV = FV ÷ (1 + r)^n
With periodic payments (annuity): FV = PMT × [((1 + r)^n − 1) ÷ r] + PV × (1 + r)^n, where r = periodic rate (I/Y ÷ compounding frequency) and n = total periods. To find PMT: PMT = [PV × r × (1 + r)^n] ÷ [(1 + r)^n − 1]. Solving for I/Y or N requires iteration (numerical methods), which the calculator handles automatically. The sign convention matters: cash outflows are negative, inflows are positive.
The number the calculator returns represents the unknown variable in your specific scenario. A solved FV tells you how much a sum grows to; a solved PV tells you what a future cash flow is worth in today's dollars; a solved PMT tells you the periodic payment required; a solved I/Y reveals the true interest rate hidden in an offer; a solved N tells you how many periods to reach your goal. Always double-check your sign convention — entering PV as positive and FV as negative (or vice versa) can flip the result.
Understanding the inputs is half the battle.
Most loans and savings accounts use ordinary annuity timing — payments occur at the end of each period. Annuity due timing — payments at the beginning — applies to lease payments, insurance premiums, and some retirement income products. The difference is one period of compounding. On a $400/month contribution at 7% over 30 years: ordinary annuity FV = $483,580; annuity due FV = $517,431 — a $33,851 difference simply from timing. The calculator handles both modes; just toggle the "Payment Timing" setting. Many users overlook this setting and get results that are off by 3–7%.
One of the most powerful but underused functions is solving for I/Y. A car dealer offers you "same as cash" financing: pay $0 now and $285/month for 48 months on a $12,500 purchase. Is that really zero percent? Enter PV = 12,500, N = 48, PMT = −285, FV = 0, solve for I/Y. The calculator returns roughly 3.8% APR — not zero. This technique unmasks the true cost embedded in payment plans, buy-now-pay-later offers, and structured settlements. It's also how you calculate the effective yield on a bond trading at a premium or discount. The US Securities and Exchange Commission and the Consumer Financial Protection Bureau both advocate for consumers to understand APR versus stated rates — knowing how to solve for I/Y is the practical skill behind that advice.
Compounding frequency: Monthly compounding at 6% APR produces a higher effective annual rate (6.168%) than annual compounding at 6%. The difference grows with the rate. This matters when comparing a savings account quoting APY versus a loan quoting APR — they use different compounding conventions by design.
Sign convention: Consistent sign convention is critical. If money going out is negative (loan payments, contributions) and money coming in is positive (loan proceeds, withdrawal), your results will be correct. Flip one sign and you'll get nonsensical output.
Real vs. nominal rates: The calculator works with nominal rates. To find real (inflation-adjusted) returns, use the Fisher equation: real rate ≈ nominal rate − inflation rate, or more precisely: (1 + nominal) ÷ (1 + inflation) − 1. Long-run US inflation averages about 3% per year historically; recent 2024 CPI was approximately 2.9%.
Time horizon: Small differences in N produce large differences in FV at high rates. An extra five years at 8% compounding monthly on a $200,000 portfolio adds roughly $95,000 in terminal value. Don't underestimate what starting early — or staying invested longer — does to the final number.
Diana, 32, wants $1,500,000 at age 67 (35 years away). She already has $45,000 in her 401(k) and expects a 7% real return. Enter: N = 420 (35 years × 12), I/Y = 7%, PV = −45,000, FV = 1,500,000. Solve for PMT: the calculator returns approximately −$838/month. That's well within the 2026 401(k) contribution limit of $24,500/year ($2,042/month), confirming the goal is feasible with consistent saving.
Carlos, 45, has $80,000 in a Roth IRA and plans to contribute $7,500/year (the 2026 IRA limit) until age 65. Assuming 8% annual return compounding monthly: N = 240, I/Y = 8%, PV = −80,000, PMT = −625 (monthly equivalent), FV = ? The calculator returns approximately $583,000 — strong confirmation that consistent IRA funding compounds powerfully over two decades.
1. Match your N and I/Y to the same frequency. If PMT is monthly, use N = total months and divide I/Y by 12 manually if your calculator doesn't auto-convert.
2. Use the sign convention consistently. Decide upfront: is "cash out" negative or positive? Apply that rule to every input.
3. Zero out fields you don't use. If there's no PMT (lump-sum problem), explicitly enter 0 rather than leaving the field with a prior value.
4. For loans, PV is positive, FV is 0. You receive the loan (positive inflow) and pay it off to zero.
5. Inflate future goals. If your target is $1M in today's dollars and inflation runs 3%, your nominal FV target in 30 years is $1M × (1.03)^30 ≈ $2.43M. Enter the nominal target.
6. Cross-check with amortization. After solving PMT on a loan, use an amortization calculator to verify total interest paid over the life of the loan.
A: A finance calculator solves for any one of the five time-value-of-money variables: present value (PV), future value (FV), periodic payment (PMT), interest rate (I/Y), and number of periods (N). You provide four known values and the calculator returns the fifth.
A: The time value of money 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 a return. It's the foundation of all discounted cash flow analysis, loan pricing, and investment valuation.
A: Present value (PV) is what a future sum of money is worth in today's dollars, discounted at a given rate. Future value (FV) is what a current sum will grow to after compounding at a given rate for a given number of periods. They're two sides of the same equation.
A: More frequent compounding produces higher effective rates for the same nominal APR. A 6% APR compounded monthly has an effective annual rate (EAR) of about 6.168%, while 6% compounded annually is exactly 6%. For savings accounts, more frequent compounding is better; for loans, less frequent is better.
A: Yes. Enter PV = loan amount (positive), N = total monthly payments (e.g., 360 for a 30-year mortgage), I/Y = annual rate, FV = 0, solve for PMT. The result is your monthly principal-and-interest payment — just add taxes, insurance, and PMI for your total housing payment.
A: A finance calculator uses compound interest, where interest earns interest each period. A simple interest calculator applies the rate only to the original principal: Interest = Principal × Rate × Time. Most real-world financial products — mortgages, credit cards, investment accounts — use compound interest.
A: Enter all known values (N, PV, PMT, FV) and leave I/Y blank. Click Calculate. The calculator uses iterative numerical methods (similar to Excel's RATE function) to find the rate that makes the equation balance. This is how you determine the true APR on any payment plan or investment.
A: An ordinary annuity has payments at the end of each period (most loans, most savings deposits). An annuity due has payments at the beginning (leases, certain insurance products). Annuity due produces slightly higher FV and slightly lower required PMT because each payment gets one extra period of compounding.
Brief disclaimer: This calculator provides estimates for educational and planning purposes only. Results depend on the accuracy of your inputs and the sign convention applied. Actual financial outcomes may differ due to fees, taxes, variable interest rates, and market conditions. This tool does not constitute financial advice. Consult a qualified financial professional for personalized recommendations.