Decreasing Annuity Immediate Calculator
Actual Decreasing Annuity Immediate Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Description
A decreasing annuity-immediate pays successively smaller multiples of a base unit.
A decreasing annuity-immediate pays successively smaller multiples of a base unit.1
In this implementation the field named actualFirstPaymentAmount is that base unit: for n payments the actual first payment is n times the field, then (n−1) times it down to one times it.
When to use Decreasing Annuity Immediate Calculator
Use this tool to apply the stated decreasing annuity immediate calculator operation with an explicit input and unit basis.
How to use Decreasing Annuity Immediate Calculator and how it works
- Establish the measurement basis and units described above.
- Enter actualEffectivePeriodInterest, actualPaymentCount, actualFirstPaymentAmount and run the tool.
- Read result.presentValue using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualEffectivePeriodInterest | Effective interest fraction for the payment period; greater than −1. | number | required; finite; further conditions in the algorithm |
| actualPaymentCount | Number of payments; integer 0–10,000. | number | required; finite; integer from 0 to 10000; further conditions in the algorithm |
| actualFirstPaymentAmount | Nonnegative payment unit P. The actual first payment is nP, despite this field’s name. | number | required; finite; nonnegative; further conditions in the algorithm |
Require i>−1, integer count 0–10,000 and nonnegative base unit P. Sum P(n−k)/(1+i)^(k+1). To model a chosen actual first payment F with n>0, supply P=F/n; zero count returns zero.
PV = sum from k=0 to n−1 of P(n−k)/(1+i)^(k+1) Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.presentValue | Discounted payment-stream total in the input payment unit. | number |
{
"input": {
"actualEffectivePeriodInterest": 0,
"actualPaymentCount": 3,
"actualFirstPaymentAmount": 1
},
"output": {
"result": {
"presentValue": 6
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Increasing Annuity Immediate Calculator. An increasing annuity-immediate pays one base amount after the first period, twice that amount after the second, and so on.
For a related operation, use Annuity Immediate Present Value Calculator. An annuity-immediate makes equal payments at the ends of successive periods.
References
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Decreasing Annuity Immediate Calculator — tool.io
Similar or alternative tools
- Increasing Annuity Immediate Calculator
An increasing annuity-immediate pays one base amount after the first period, twice that amount after the second, and so on.
- Annuity Immediate Present Value Calculator
An annuity-immediate makes equal payments at the ends of successive periods.