Calculating Reducing Daily Pro Rata Amounts

Dec 5, 2011

Here's my problem.

Charter default premium is a calculated as a rate on outstanding charter hire.

Therefore if charter period is 1 year and daily hire is 20,000, outstanding charter hire (policy limit) at inception would be 20,000 x 365 = $7,300,000

However, by day 365 outstanding charter hire and prevailing policy limit would only be 20,000 x 1 day = $20,000

The premium is calculated on a daily pro rata basis on the reducing outstanding amounts.

I've calculated the premium on the attached spreadsheet assuming hire is monthly not daily, but it would be too laborious to try and calculate that for 12 months or more on a daily basis. What I'm hoping is that there's a formula, covering the range of data, presumably using the calculation on the first day and the last day, but which cuts out all the intermediate steps.

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