Annuity Calculator

Annuity is evaluated from Regular Payment Amount, Annual Interest Rate and Number of Years. The calculation reports Future Value, Present Value and Total Payments Made.

Results

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About the Annuity Calculator

Annuity is treated here as a quantitative relation between Regular Payment Amount, Annual Interest Rate, Number of Years and Payment Frequency and Future Value, Present Value, Total Payments Made and Total Interest Earned.

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:
Future Value (Ordinary Annuity) = PMT x [(1+r)^n - 1] / r
Future Value (Annuity-Due) = FV_ordinary x (1+r)
Present Value (Ordinary Annuity) = PMT x [1 - (1+r)^ - n] / r
Present Value (Annuity-Due) = PV_ordinary x (1+r)
Where r = periodic rate, n = total periods, PMT = payment per period

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:

Future Value (Ordinary Annuity) = PMT x [(1+r)^n - 1] / r
Future Value (Annuity-Due) = FV_ordinary x (1+r)
Present Value (Ordinary Annuity) = PMT x [1 - (1+r)^ - n] / r
Present Value (Annuity-Due) = PV_ordinary x (1+r)
Where r = periodic rate, n = total periods, PMT = payment per period

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: Retirement Savings Accumulation

Inputs

payment: 1000 annual_rate: 7 years: 30 frequency: 12 annuity_type: ordinary
Future Value: $1,219,971. Present Value: $150,307.57. Total Payments Made: $360,000. Total Interest Earned: $859,971

With Regular Payment Amount = 1,000, Annual Interest Rate = 7, Number of Years = 30 and Payment Frequency = 12 as the stated inputs, the result is Future Value = $1,219,971, Present Value = $150,307.57 and Total Payments Made = $360,000. Each value corresponds to the declared output fields.

Example 2: Immediate Annuity — Retirement Income

Inputs

payment: 2500 annual_rate: 5 years: 20 frequency: 12 annuity_type: ordinary
Future Value: $1,027,584.17. Present Value: $378,813.28. Total Payments Made: $600,000. Total Interest Earned: $427,584

With Regular Payment Amount = 2,500, Annual Interest Rate = 5, Number of Years = 20 and Payment Frequency = 12 as the stated inputs, the result is Future Value = $1,027,584.17, Present Value = $378,813.28 and Total Payments Made = $600,000. Each value corresponds to the declared output fields.

Example 3: Annuity-Due — Lease Comparison

Inputs

payment: 1500 annual_rate: 6 years: 3 frequency: 12 annuity_type: due
Future Value: $59,299.18. Present Value: $49,553.06. Total Payments Made: $54,000. Total Interest Earned: $5,299

With Regular Payment Amount = 1,500, Annual Interest Rate = 6, Number of Years = 3 and Payment Frequency = 12 as the stated inputs, the result is Future Value = $59,299.18, Present Value = $49,553.06 and Total Payments Made = $54,000. Each value corresponds to the declared output fields.

Example 4: Quarterly Pension Drawing

Inputs

payment: 7500 annual_rate: 4.5 years: 25 frequency: 4 annuity_type: ordinary
Future Value: $1,373,953.63. Present Value: $448,867.97. Total Payments Made: $750,000. Total Interest Earned: $623,954

With Regular Payment Amount = 7,500, Annual Interest Rate = 4.5, Number of Years = 25 and Payment Frequency = 4 as the stated inputs, the result is Future Value = $1,373,953.63, Present Value = $448,867.97 and Total Payments Made = $750,000. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate how much an annuity will pay in retirement
  • Find the present value of a future stream of annuity payments
  • Compare an annuity purchase to other retirement income strategies