Worked-example setupScope and assumptions
- Both alternatives contain exactly four annual $6,000 payments and use the same supplied 5 percent annual periodic rate.
- Only every payment date shifts one year earlier in the due alternative.
- Period
- Four equal annual payment intervals
- Units
- USD at the month-zero valuation date and decimal rate per year
- Rounding
- Retain full precision; display currency to cents.
The ordinary alternative pays at years 1 through 4. The due alternative pays at years 0 through 3. Neither has five payments.
ordinary PV = $6,000 × [1 - (1.05)^(-4)] / 0.05
= $21,275.7030…
due PV = ordinary PV × 1.05
= $22,339.4882…
At the same positive rate, the due stream has the higher value because every payment occurs one period earlier. The $1,063.79 displayed difference is a timing effect under the model, not evidence that either contract has better service, lower risk, or preferable legal terms.
Verified calculation · time value analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- annuities
- 2 fields
Inspect data
{
"due_service": {
"payment": 6000,
"periodic_rate": 0.05,
"periods": 4,
"timing": "due"
},
"ordinary_service": {
"payment": 6000,
"periodic_rate": 0.05,
"periods": 4,
"timing": "ordinary"
}
}Recomputed result
| Measure | Value |
|---|---|
| due service future value | 27,153.7875 |
| due service present value | 22,339.4882 |
| ordinary service future value | 25,860.75 |
| ordinary service present value | 21,275.703 |