Interactive MTA/New York MetroCard Calculator to Avoid Overpaying

 
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Below, I outline the methods used in the above chart for avoiding leftover amounts when purchasing rides on a MetroCard, as well as thresholds for purchasing unlimited rides for both 7-day and 30-day passes.


MTA MetroCard Information and Cost Optimization

The Metrocard bonus adds 5% to the total purchase price, which can be represented as follows:


where T is the total added to the MetroCard, P is the amount paid, and the 1.05 is the total plus the added 5%.

Therefore, if we want to purchase 5 rides and avoid having leftover change on the MetroCard, we need to calculate the approximate amount (in multiples of $0.05 per MTA's requirement) to add to the card to get closest to the cost of 5 rides while also incorporating the extra 5%. This can be calculated in the following manner:
where Π is the total added to the MetroCard, n is the total number of rides, C is the price per ride. If we input 5 as n and $2.75 for C, we can calculate the amount needed to minimize the leftover change:

And if we insert this total back into the equation above using the total above (using only multiples of $0.05 as the P above), we get:


So we follow all of MTA's rules (multiples of $0.05, 5% bonus) and we end up with only $0.01 leftover. If you want to test this, you can go to MTA's website and see their bonus calculator here or check out another calcualtor here (by panix.com).

NOTE:

Remember to always round -UP- when calculating the total for the desired number of rides, otherwise you will end up with a large amount left over just shy of another ride.

Interactive MTA/New York MetroCard Calculator Description

Using the method above and an algorithm that optimizes cost and unlimited ride options, I created the interactive chart at the top of this page that shows subway riders when to buy single purchase amounts, 7-day unlimited passes, and 30-day unlimited passes. For cases beyond 7 days in the city, I have also included an optimized mix of single pay options and 7-day options. For amounts greater than the 30-day unlimited cost, I have recommended the 30-day unlimited pass. In every case, the chart shows the rider which option is financially advantageous based on the days in the city and rides per day.

MTA_calculator_example.gif

See More in Programming and Python:

Joshua Hrisko

Maker Portal is a blog-centric company intended for young innovators interested in real-world applications to engineering. Resources include: physical products, mobile applications, software development, e-learning, and blog-style article writing. The maker-based approach is explored using written articles with topics ranging from Raspberry Pi, heat transfer, acoustics, robotics, data analysis, Arduino, sensor design, Python programming, and much more. Difficulty levels range depending on the topic and there is extensive focus on open-source software implementation, however, there will be articles with a focus on software design as well. The intention is to demonstrate applications of engineering that are repeatable at the intermediate level without requiring colossal resources. 

https://makersportal.com/
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