Expenential Equation for providing price quotes

[noy2014]

I am really stuck! I believe there is an answer to my problem, it is just beyond me.

I have vacation rental property. I normally do the price quotes for potential guests by hand. I would like to automate this process with a web-based application, but I can not figure out the formula for the discount that I apply to extended stay. I have a fixed daily rate for various property units, but I need a formula to determine the discount rate applied to the total of the sum of the daily rate.

These are the factors I currently recognize;
1) 0 - 5 days stay, there is no discount applied.
2) 6 day stay, has a fixed discount (currently $200).
3) 7 - 14 day stay has a $75 per day discount. (ie. 5 day = $525 OFF)

So far, no problem. Here is where it gets tricky. 14 - 31 days, needs a sliding scale discount rate applied to the sub-total, to yield the desired total rate.

- The more days stay, allow for a greater per day discount.
- I would indicate a pre-determined minimum and maximum rate for the 15 - 31 day stay respectively.
- The new average daily rate would then exponential decrease. Consequentially, the calculated discount rate would exponential increase daily.
- This formula should incorporate the prior days discount rate, and increase it by another pre-determined fixed rate (let's call it "Y"). Staying within the Maximum 31 day rate.
- I am open to the any variable "Y" figure that the discount and/or avg.-daily rate would increase/decrease by. This "Y" figure I would be able to play with to adjust the increasing discount distribution.

I put together this following webpage to chart the example of what I am trying to accomplish: http://rentflamingo.com/discount_formula.htm

Please note that on day 15 and 31, the discount applied to the Sub-Total would reflect the pre-determined the minimum and maximum value. It is the yellow highlighted area in between that I need a formula to calculate.

Well, I tried to be as descriptive as possible. If I was not clear about something in particular, please feel free to contract me. Any assistance would be so greatly appreciated

Best Regards-
Noy

 

[mmm4444bot]

$300 reflects a 23.08% discount on $390.

$194 reflects a 50.26% discount on $390.

The following exponential formula gives the discount off of the regular daily rate for each stay beginning with 15 days and ending with 31 days.

\(\displaystyle \text{discountRate} \; = \; 0.2308 \cdot e^{0.0486 \cdot (\text{dayNumber} - 15)}\)

For example, when the stay is 22 days, then dayNumber = 22

\(\displaystyle \text{discountRate} \; = \; 0.2308 \cdot e^{0.0486 \cdot (22 - 15)} \; = \; 0.3243\)

$264 relects a 32.43% discount on $390.

IF dayNumber < 6 THEN discountRate = 0
  ELSE
  IF dayNumber < 7 THEN discountRate = 0.0846
    ELSE
    IF dayNumber < 15 THEN discountRate = 0.1923
      ELSE
      IF dayNumber < 32 THEN discountRate = 0.2308 * e^[0.0486 * (dayNumber - 15)]
        ELSE
        DISPLAY pleaseCallMessage

What do I pay when I stay more than 31 days?

Cheers,

~ Mark