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A Case of Saving Money by Spending More

Posted in Personal, and Travel

THE DANISH REJSEKORT is an electronic payment system used in most danish public transportation systems like buses, trains and subways. Its an electronic card that comes in two variants: an anonymous edition where you manually deposit fare money by a kiosk system. The second edition is personalized and offers an online management system with option of association to a payment card (Dankort, VISA, Master card etc). This personal edition also offers a discount system which is intended to give the Rejsekort a price competitive incentive compared to single ticket purchases.

I commute a pretty long way to work. First i drive in my car about 25 km to the train station. There i take the train for an hour, switches train and ride another hour before i then walk the last 1.5 km to the office.

A discount system would be expected to benefit a person like me, which is riding public transportation for just about four hours a day. And it does, but not a much as one would expect (at first).

I jump on the first train 06:55 o’clock. This triggers the first discount system. Traveling outside the busiest hours gives a discount. My fare price is therefore

160 \,[kr] \rightarrow 128 \,[kr]

This is however not true for my trip home. This gives a total daily travel cost of:

128 + 160 = 288 \,[kr]

I only do the train ride three days a week (i take the car other days).

This makes my monthly cost:

288 \,[kr] * 3 \,[á/week] * 4 \, [week] = 3456 \,[kr]

That is a pretty huge dent in the monthly budget. Fortunately a second parameter of the discount system is available. A level system is defined. It goes a this:

Customer/discount level 0 1 2 3 4 5 6 7
Adult – Rejsekort personal 0% 10% 10% 25% 25% 25% 40% 40%

The above discount system is not based on fare prices, distance, stops or zones but on the amount of rides alone.

The formula for the discount level is as follows:

discount\; point = (amount \; of \; travels * 10)

(another formula translate discount points to discount level). With this system i reach discount level 3. This changes my monthly cost:

3456 \,[kr] - 25 \% = 2592 \,[kr]

Okay. Now this is where the bonus system gets pretty weird – or perhaps just flawed. Remember how the discount system is not based on the price but amounts of travels alone? Increasing the amount of travels will bump you to a higher discount level, and at my monthly cost this can mean a significant saving. As the discount formula ignores ticket price, i can clime the discount latter by taking the cheapest possible ride. To reach next percentage level i need 10 more rides. Lets see where that brings me:

A public bus stops a few hundred meters away from my home. The next stop is an additional few hundred meters further way. As i am already at discount level 3, i got 25 % discount from get go. The ticket fare is 13.95 kr before this.

10 \,[ride] * (13.95 \,[kr/ride] - 25 \%) = 105 \,[kr]

Having achieved a discount level that gives a 40% discount, my monthly travel cost to work will then reduce to:

3456 \,[kr] - 40 \% = 2074 \,[kr]

Adding the extraneous trips, the total monthly travel cost will be:

2074 + 105 = 2179 \,[kr]

Thus by traveling more, i save:

2592 - 2179 = 413 \,[kr]

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