I am trying to work out how to set rates for a rental business problem.

If a car or other item was to be rented for say $160 a week (7 days) and one wanted to set the rates for rental up to 14 days - how would you work out what to charge for the daily rate versus for 2 days, 3 days, 4 days and up to 14 days?
Presumably you would want the rate for 1 day to be high in comparison to a weekly or 2-weekly rental (ie the longer you rent it, the cheaper (relatively) it would be? can anyone give me a working formula to work this out based on the cost of the weekly rental? please help! Thanks!

It depends entirely on how much cheaper you want the rate per week (more precisely, the pro rata rate per day) to be relative to the rate for 1 day .....

For example:

1 day = $20

2 days = $20 + (0.9)($20) = ....

3 days = $20 + (0.9)($20) + (0.9)^2($20) = ....

etc.

In which case you need the formula for the sum of a geomtric series.

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can you explain that in math for dummies? say i wanted the daily rate to be $40 and the weekly rate to be $160 - how would I work that out?
PS - Thanks for your time!

It is completely arbitrary and depends on what prices you want to set for each day.

40, 35, 30, 25, 18, 7, 5

is just one of the hundreds of ways of doing it.

__________________
There are two things you should never try to prove ...... the impossible and the obvious.

Lack of planning on your part does not constitute an emergency on my part.

Pressure makes diamonds.