Enter the total period (in years), the discount rate, and the replacement interval. Optionally enter the unit cost to get the total present value. The calculator returns the multiplier for an item bought once every a years over a total period of b years: it sums the discount factor (1 + r)−t at each replacement time t = a, 2a, 3a, … up to the highest multiple of a that is ≤ b. Tick “immediate purchase” to include a £1 contribution at t = 0 (i.e. the first item is being bought now). For a schedule of several recurring items on different cycles, use the item-by-item build-up below the single calculator: add a row per item and the table totals each item's cost × its own multiplier.
Multipliers for Fixed Periods and Intervals
Multipliers for a pecuniary loss paid for a fixed period (and at intervals other than yearly) at a chosen discount rate. Computed live from the formula, so any term and rate is supported — not limited to those in published tables.
Multiplier
—
Total value of loss
—
Item-by-item build-up (aids & appliances)
For a schedule of recurring items — wheelchairs, prostheses, hearing aids and batteries — each replaced on its own cycle. Set the total period and discount rate once, add a row per item, and the table looks up each item's multiplier and totals the lot.
#
Item
Unit cost (£)
Replace every (yrs)
Applies for
Buy now?
Multiplier
Item total
Grand total
—
Show working
Method:Each item is treated as a recurring purchase. The calculator counts the replacements that fall within the item's applicable period (the whole period, or a discrete sub-period) and sums the discount factor at each replacement date. “Buy now?” adds a £1 contribution at t = 0. The item total is its unit cost × its multiplier.
Formula:Multiplier = [1 if bought now] + Σ (1 + r)−t for t = a, 2a, 3a, … ≤ period
Discount rate:—
Total period:—
Item breakdown
Item
Unit cost
Every (yrs)
Applies for
Replacements
Multiplier
Subtotal
The multiplier counts only whole replacement cycles completed within the applicable period (a partial final cycle is not bought). Use “Buy now?” where the first item is purchased at the outset rather than after one interval.
Source: present-value formula on the chosen personal-injury discount rate; consistent with Ogden Table A5 for whole-period replacements.