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Miraç Özdemir
Compound Interest

Present Value and Future Value Calculator

Time value of money: solve for future value, present value, the required interest rate or the required number of periods with compound interest.

Version 1

Things to keep in mind:

  • Taxes, fees and inflation are ignored; results are gross nominal values.
  • The rate is assumed constant for the whole period; with floating rates results deviate.
  • The present value must be above 0 when solving for rate or periods, and the rate must not be 0 when solving for periods (the calculation returns an error).

Calculator

Time value of money

Choose the unknown. Fill in the other three fields; the field for the unknown is ignored.

TRY

Amount today. Must be greater than 0 when solving for the rate or periods. Ignored when solving for it.

TRY

Amount at the end. Used when solving for present value, rate or periods; ignored when solving for it.

Compound rate of each period (month, year, …). Must be above 0 when solving for periods, and in the same unit as the period count.

Number of compounding periods (months, years, …); decimals allowed. Ignored when solving for it.

After the first calculation, the result updates automatically when you change a value.

Result

Enter the values and press Calculate to see the result here.

About this tool

The time value of money means an amount today grows with interest and is worth more in the future. This tool solves for one of four unknowns from the other three.

Formulas (r = rate per period, n = number of periods)

  • Future value: FV = PV × (1 + r)^n
  • Present value: PV = FV / (1 + r)^n
  • Required rate: r = (FV / PV)^(1/n) − 1
  • Required periods: n = ln(FV / PV) / ln(1 + r); the whole periods rounded up are shown too
  • Total change = FV − PV

Rate and period must share the same unit: a monthly rate needs periods in months, an annual rate needs years. Amounts are rounded HALF_UP to 2 decimals, rate and periods to 4.

Example 1 — future value

100,000 growing for 12 periods at 3% per period reaches 100,000 × 1.03^12 = 142,576.09; total change 42,576.09.

Example 2 — present value

To hold 500,000 in 3 years at 40% a year you need 500,000 / 1.4^3 = 182,215.74 today; total change 317,784.26.

Example 3 — required rate and periods

Turning 250,000 into 1,000,000 in 5 periods requires 31.9508% per period (4^(1/5) − 1). Turning 100,000 into 300,000 at 25% per period takes 4.9233 periods, or 5 whole periods.

How to read the result

Future value is the nominal amount today's sum reaches at term end at a constant rate; present value is today's equivalent of a future amount and falls as the discount rate rises. Total change (interest earned) is the difference between the two. In the rate or periods modes, the result is the constant condition needed to reach the target; since real rates may change, read it as an approximation. Taxes, fees and inflation are not included.

How to use

  1. Choose what to calculate (future value, present value, rate or periods).
  2. Fill in the other three fields.
  3. Enter the rate and the period count in the same unit.
  4. Press Calculate.

Notes

Amounts are rounded HALF_UP to 2 decimals, rate and periods to 4. The number of periods may be fractional. There are no recurring payments; a single lump sum is assumed. The field of the unknown is ignored.

Sources

Frequently asked questions

4 questions

  1. Multiply today's amount by (1 + rate per period)^number of periods. For example 100,000 at 3% a month for 12 months becomes 142,576.09. The rate is assumed constant and tax and inflation are ignored.

Next step

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