Present Value Calculator

Present Value is evaluated from Future Value, Annual Discount Rate and Number of Years. The calculation reports Present Value, Discount Amount and Total Discount.

Results

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About the Present Value Calculator

Present Value is treated here as a quantitative relation between Future Value, Annual Discount Rate, Number of Years and Compounding Frequency and Present Value, Discount Amount and Total Discount.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
PV = FV / (1 + r/n)^(n x t)
- FV = future value
- r = annual discount rate (decimal)
- n = compounding periods per year
- t = number of years
Discount Amount = FV - PV
Discount% = (FV - PV) / FV x 100

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

PV = FV / (1 + r/n)^(n x t)
- FV = future value
- r = annual discount rate (decimal)
- n = compounding periods per year
- t = number of years
Discount Amount = FV - PV
Discount% = (FV - PV) / FV x 100

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Lottery Lump Sum Analysis

Inputs

future_value: 1000000 annual_rate: 7 years: 20 compounding: 1
Present Value: $258,419. Discount Amount: $741,581. Total Discount: 74.2%

With Future Value = 1,000,000, Annual Discount Rate = 7, Number of Years = 20 and Compounding Frequency = 1 as the stated inputs, the result is Present Value = $258,419, Discount Amount = $741,581 and Total Discount = 74.2%. Each value corresponds to the declared output fields.

Example 2: Inheritance in 10 Years

Inputs

future_value: 250000 annual_rate: 6.5 years: 10 compounding: 1
Present Value: $133,181.51. Discount Amount: $116,818.49. Total Discount: 46.7%

With Future Value = 250,000, Annual Discount Rate = 6.5, Number of Years = 10 and Compounding Frequency = 1 as the stated inputs, the result is Present Value = $133,181.51, Discount Amount = $116,818.49 and Total Discount = 46.7%. Each value corresponds to the declared output fields.

Example 3: Bond Present Value

Inputs

future_value: 50000 annual_rate: 4.5 years: 5 compounding: 12
Present Value: $39,942.62. Discount Amount: $10,057.38. Total Discount: 20.1%

With Future Value = 50,000, Annual Discount Rate = 4.5, Number of Years = 5 and Compounding Frequency = 12 as the stated inputs, the result is Present Value = $39,942.62, Discount Amount = $10,057.38 and Total Discount = 20.1%. Each value corresponds to the declared output fields.

Example 4: Business Investment — Hurdle Rate Test

Inputs

future_value: 150000 annual_rate: 12 years: 3 compounding: 1
Present Value: $106,767.04. Discount Amount: $43,232.96. Total Discount: 28.8%

With Future Value = 150,000, Annual Discount Rate = 12, Number of Years = 3 and Compounding Frequency = 1 as the stated inputs, the result is Present Value = $106,767.04, Discount Amount = $43,232.96 and Total Discount = 28.8%. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate today's value of a future inheritance or settlement
  • Determine if an investment is worth making based on future returns
  • Compare different future payment streams in today's dollars