Time Value of Money (TVM) Calculator – Calculate FV, PV & Payments Period

Online TVM Calculator

Use the Time Value of Money calculator below to see how your money can grow over time. Simply enter your present value (PV), future value (FV), interest rate, number of periods, and any recurring payments, and the calculator will instantly show your results. It’s a quick way to plan savings, evaluate loans, or figure out how much you need to invest to reach your financial goals.

Definition: The Time Value of Money calculator is a financial tool that computes how the value of money changes over time because of interest. It can find future value, present value, interest rate, number of periods, or repeating payment amounts based on the inputs you supply.

What Is Time Value Of Money (TVM)?

Time Value of Money (TVM) is the principle that a sum of money today is worth more than the same nominal sum at a future date because money available now can be invested to earn interest. In short: money now has earning potential; money later does not — unless it grows by interest. TVM underlies decisions about saving, borrowing, investing, loan amortization, and retirement planning.

How TVM Works

At its core TVM compares present amounts and future amounts using an interest rate per period. There are four basic components:

• Present Value (PV): the value now.
• Future Value (FV): the value at some future date.
• Interest rate (r): the rate per period (expressed as a decimal, so 5% → 0.05).
• Number of periods (N): how many compounding periods occur.
• Payment (PMT): a repeating contribution or withdrawal each period (can be zero).

Two standard cases:

• Single lump sum: PV grows to FV by compounding.
• Repeating payments plus lump sum: payments add to growth and are treated with an annuity factor.

Our TVM calculator assumes payments occur at the end of each period (ordinary annuity) and uses standard discrete compounding formulas.

How to Use The Time Value of Money (TVM) Calculator

1. Choose what you want to solve for: Future Value, Present Value, Interest Rate, Periods, or Repeating Payment.
2. Enter the known values:
   • If solving FV: enter PV, interest rate (as %), number of periods, and optionally PMT.
   • If solving PV: enter FV, interest rate, number of periods, and optionally PMT.
   • If solving rate: enter PV, FV, number of periods, and optionally PMT.
   • If solving periods: enter PV, FV, interest rate, and optionally PMT.
   • If solving payment: enter PV, FV, interest rate, and number of periods.
3. Make sure rates are per period (e.g., monthly rate if periods are months).
4. Click Calculate.
5. Read the output in the results area. Payment results are shown as absolute amounts (the calculator reports the payment magnitude).

Notes and tips:

• Enter rates as percentages (5 means 5% → internally converted to 0.05).
• If interest is 0 (zero rate), special-case arithmetic is used (no compounding).
• When solving for rate or periods, the calculator uses numerical methods; some input combinations may not yield a solution (for example, inconsistent PV/FV relative to PMT and rate). If no solution exists, the calculator will indicate that.

TVM Calculation Formula

All formulas below use r as the interest rate per period (in decimal form — e.g., 5% = 0.05) and N as the number of periods.

Future value (with periodic payments at end of period):

Special case when r = 0: FV = PV + PMT × N

Present value (with periodic payments at end of period):

Special case when r = 0: PV = FV − PMT × N

Repeating payment (PMT) required to reach FV after N periods:

Special case when r = 0: PMT = (FV − PV) ÷ N

Notes on notation:

• (1 + r)ⁿ means (1 + r) raised to the power n.
• PMT is assumed to be the amount contributed at the end of each period (ordinary annuity).
• Percent inputs must be divided by 100 to obtain r in decimal form.

These formulas match the arithmetic used by the TVM calculator above.

TVM Example Calculations

Below are worked examples that show how the formulas are applied and what results the online TVM calculator above will return.

Example A: Future Value with regular payments

Inputs:

• PV = $1,000
• Annual interest rate r = 5% → r = 0.05 per period
• N = 10 periods
• PMT = $100 per period

Formula:

Step-by-step (rounded for presentation):

1. (1 + r)ⁿ = (1.05)¹⁰ ≈ 1.628894627
2. PV × (1 + r)ⁿ = 1,000 × 1.628894627 ≈ 1,628.89
3. ( (1 + r)ⁿ − 1 ) ÷ r = (1.628894627 − 1) ÷ 0.05 ≈ 12.57789254
4. PMT × that factor = 100 × 12.57789254 ≈ 1,257.79
5. FV ≈ 1,628.89 + 1,257.79 = 2,886.68

Result:

• Future Value ≈ $2,886.68

Example B: Future Value starting from zero with small rate

Inputs:

• PV = $0
• r = 3% → 0.03
• N = 5
• PMT = $200

Computation (summary):

1. (1.03)⁵ ≈ 1.159274
2. PV term = 0
3. Annuity factor = (1.159274 − 1) ÷ 0.03 ≈ 5.796
4. FV ≈ 200 × 5.796 = 1,159.83

Result:

• Future Value ≈ $1,061.83

Example C: Present Value of a future lump sum

Inputs:

• FV = $5,000
• r = 6% → 0.06
• N = 4
• PMT = $0

Formula:

Computation:

1. (1.06)⁴ ≈ 1.26247696
2. PV ≈ 5,000 ÷ 1.26247696 ≈ 3,960.47

Result:

• Present Value ≈ $3,960.47

Example D: Payment required

Find PMT required to grow PV = $1,000 to FV = $2,000 in N = 5 periods with r = 4%.

Inputs:

• PV = $1,000
• FV = $2,000
• r = 0.04
• N = 5

Formula:

Computation:

1. (1.04)⁵ ≈ 1.2166529
2. PV × (1 + r)ⁿ ≈ 1,216.65
3. FV − that = 2,000 − 1,216.65 ≈ 783.35
4. Denominator (1.2166529 − 1) ≈ 0.2166529
5. PMT ≈ 783.35 × 0.04 ÷ 0.2166529 ≈ 144.63

Result:

• Payment ≈ $144.63 per period

Example: Number of periods required (solving for N)

Find N so that PV = $1,000 grows to FV = $2,000 at r = 5% with no additional payments (PMT=0).

Formula (for lump sum) can be rearranged:

Computation:

1. FV ÷ PV = 2.0
2. log(2.0) ÷ log(1.05) ≈ 14.2067

Result:

• N ≈ 14.21 periods

What Is Future Value

Future Value (FV) is the amount an investment will grow to after earning interest for a number of periods. FV collects the compound growth of the initial principal plus any stream of periodic payments. When you plan savings or retirement, FV answers: “If I invest this amount now and add X every period, what will I have later?”

What Is Present Value

Present Value (PV) is the value today of a sum that will be received or paid in the future. PV discounts future amounts back to today using the interest rate per period. When comparing project cash flows, PV lets you compare apples-to-apples: money now vs money later.

How Is Interest Calculated In TVM

Interest is applied per period based on the stated rate r:

• For compounding once per period: each period the balance is multiplied by (1 + r).
• Compound growth after N periods is (1 + r)ⁿ.
• When payments occur each period, their accumulated contribution is the payment multiplied by the annuity accumulation factor: ( (1 + r)ⁿ − 1 ) ÷ r.

Important practical points:

• Use consistent units: if the rate is annual and compounding is monthly, convert the annual rate to a monthly rate and convert years to months.
• The calculator treats the given rate as the rate per period; conversion is up to the user.

How to Calculate TVM Manually

A basic step-by-step manual approach for a common need — compute FV with periodic payments:

1. Convert interest percentage to decimal: r = rate% ÷ 100.
2. Compute (1 + r)ⁿ.
3. Multiply PV by (1 + r)ⁿ.
4. Compute annuity factor: ( (1 + r)ⁿ − 1 ) ÷ r.
5. Multiply annuity factor by PMT.
6. FV = PV term + PMT term.

For PV from FV:

1. Compute (1 + r)ⁿ.
2. Compute annuity factor as above.
3. PV = (FV − PMT × annuity factor) ÷ (1 + r)ⁿ.

For small or zero r, use the special-case linear formulas (no compounding). For solving rate or periods where algebra is not straightforward, a numerical method (iteration, bisection, or software solver) is used.

FAQs About TVM

Q: Does the calculator assume payments happen at the beginning or end of a period?
A: It assumes payments occur at the end of each period (ordinary annuity). If payments are at the beginning, multiply the annuity factor by (1 + r).

Q: How should I enter the interest rate?
A: Enter the interest rate as a percentage (for example enter 5 for 5%); the calculator converts to decimal (0.05) internally.

Q: What if the interest rate is zero?
A: Use the simplified formulas: FV = PV + PMT × N and PV = FV − PMT × N. The calculator automatically handles this special case.

Q: Why might the calculator say “rate could not be determined”?
A: Solving for rate may require numerical root-finding. If the inputs are inconsistent (for example the direction of cash flows cannot produce the target FV), the solver may not find a valid rate. Try checking signs and feasibility of inputs.

Q: Are payments assumed positive or negative?
A: Payments are treated as periodic contributions in the formulas. The calculator reports payment amounts as absolute values in the results for clarity. When modeling loans, follow a consistent sign convention (e.g., PV as loan proceeds positive and periodic payments as outflows) or use the absolute result as the required payment amount.

Q: What compounding frequency does the calculator use?
A: The calculator uses the rate as the per-period rate. To model monthly compounding with an annual interest rate, divide the annual rate by 12 and use periods in months.

Conclusion and Best Practices

The Time Value of Money is a foundational finance concept: money now is worth more because of the ability to earn interest. The calculator above simplifies routine computations — future value, present value, interest rate, periods, and payment — using well-known discrete compounding formulas and numerical solvers when needed.

Best practices:

• Keep units consistent: match rate and periods (monthly rate with months, yearly rate with years).
• Double-check sign conventions when modeling loans versus savings.
• Use the special zero-rate formulas when interest is zero.
• For planning, test several scenarios (different rates and payment sizes) to see how sensitive results are to assumptions.
• When results seem implausible, check inputs for typos (decimal vs percent, periods vs years).

With these formulas and an understanding of how the time value of money calculator above works, you can compare savings plans, evaluate loans, and make better financial decisions based on time-adjusted values of money.