Metro card fare mathematical puzzler

[TCurtin]

Here's a puzzler (although admittedly an accounting question rather than anything to do with rail operations)

According to the pricing that went into effect 1/1/11 when you purchase a Metro Card you get 7% bonus instead of the former 15%. With the former pricing the magic number to buy was $45.00, which with the 15% bonus gave you $51.75, EXACTLY 23 rides. Thus you could discard a used-up card without leaving any money on the table.

Now the bonus is 7%. A little work with a spreadsheet will show you there is NO amount you can buy a card for that will give you an EXACT number of rides with nothing left. The best you can do --- because the vending machines only accept whole dollar transactions --- is purchase a card for $61.00 that will give you 29 rides and leave $.02 on the table.

Anybody have any more clever ideas? There may be some way to make two successive purchases on the same card and have it come to an exact multiple of $2.25.

This is a not-so-subtle, intentional ploy to raise revenue --- all those odd cents left over on every metro card purchase will put quite a lot of additional revnue into the MTA's coffers over the course of a year!

This is the kind of stuff you think about when living in Manhattan on a retiree budget. The good news is that I only have to worry about it for another 7 months at which time I will qualify for a seniors-rate easy pay card.

[mrsam]

Well, if you buy $225 worth of fares, the 7% bonus gets you $240.75 on the card, or 107 rides @2.25.

[Allan]

Here's a puzzler (although admittedly an accounting question rather than anything to do with rail operations)

According to the pricing that went into effect 1/1/11 when you purchase a Metro Card you get 7% bonus instead of the former 15%. With the former pricing the magic number to buy was $45.00, which with the 15% bonus gave you $51.75, EXACTLY 23 rides. Thus you could discard a used-up card without leaving any money on the table.

Now the bonus is 7%. A little work with a spreadsheet will show you there is NO amount you can buy a card for that will give you an EXACT number of rides with nothing left. The best you can do --- because the vending machines only accept whole dollar transactions --- is purchase a card for $61.00 that will give you 29 rides and leave $.02 on the table.

Anybody have any more clever ideas? There may be some way to make two successive purchases on the same card and have it come to an exact multiple of $2.25.

This is a not-so-subtle, intentional ploy to raise revenue --- all those odd cents left over on every metro card purchase will put quite a lot of additional revnue into the MTA's coffers over the course of a year!

This is the kind of stuff you think about when living in Manhattan on a retiree budget. The good news is that I only have to worry about it for another 7 months at which time I will qualify for a seniors-rate easy pay card.

I beg to differ.

I, too did some work with a spreadsheet and $35.75 with 7% bonus ($2.50) will give you $38.25 which equals 17 fares with nothing left over. The same apples to $37.85. The 7% bonus ($2.65) will give you $40.50 which covers 18 fares with nothing left over. One more: $39.95 with the 7% bonus ($2.80) will equal $42.75 which covers 19 fares with nothing left over.

What I have been doing lately is buying a $20.00 card (with bonus = $21.40) and adding $1.10 to it to make $22.50 for 10 fares (or when I am at the Transit Museum store buying a $21.03 card which with bonus equals $22.50).

BTW - on the old 15% bonus the minimum was $15.65 which with the bonus equaled $18.00 which covered 8 fares with nothing left over.


[To be on the safe side - I verifed my spreadsheet work here: http://www.metrocardbonuscalculator.com/]

[modorney]

Isn't the card refillable? And don't you get the bonus when you refill the card?

I see what you are trying to do, have the card come out "even". We have a similar situation on San Fran's BART. Kid and senior tickets are cheaper, and come with a discount. But these aren't refillable cards, they are non-refillable paper tickets. But, with BART's fares based on distance, you can always get off part way , and get back on (that is, go out the faregate and come back in). Most of the time this costs you a little, but a few places, you save some money.

[Allan]

Isn't the card refillable? And don't you get the bonus when you refill the card?

I see what you are trying to do, have the card come out "even". We have a similar situation on San Fran's BART. Kid and senior tickets are cheaper, and come with a discount. But these aren't refillable cards, they are non-refillable paper tickets. But, with BART's fares based on distance, you can always get off part way , and get back on (that is, go out the faregate and come back in). Most of the time this costs you a little, but a few places, you save some money.

There are advantages to having a fixed fare system.

Yes, the card is refillable but it would be quite a while before the bonuses adds up to a full fare ($2.25).

I, for one, prefer to have my cards come out even.


As far as BART goes, the Clipper card is refillable. Maybe if enough people complain, they will have a reduced fare option on BART for the Clipper card instead of people having to use the Green, Orange or Red paper ticket.

[TCurtin]

I did some work with a spreadsheet and $35.75 with 7% bonus ($2.50) will give you $38.25 which equals 17 fares with nothing left over. The same apples to $37.85. The 7% bonus ($2.65) will give you $40.50 which covers 18 fares with nothing left over. One more: $39.95 with the 7% bonus ($2.80) will equal $42.75 which covers 19 fares with nothing left over.

What I have been doing lately is buying a $20.00 card (with bonus = $21.40) and adding $1.10 to it to make $22.50 for 10 fares (or when I am at the Transit Museum store buying a $21.03 card which with bonus equals $22.50).

BTW - on the old 15% bonus the minimum was $15.65 which with the bonus equaled $18.00 which covered 8 fares with nothing left over.


[To be on the safe side - I verifed my spreadsheet work here: http://www.metrocardbonuscalculator.com/]

I figured out the same thing on my spreadsheet but
I had a few attempts to purchase a card for anything but "whole dollars" rejected by the veding machine. I must admit I didn't specifically try 35.75 or 37.85 --- perhaps the machines are "programmed" to accept those specific amounts. Your experience with the Transit Museum store is interesting . . .

[Allan]

I did some work with a spreadsheet and $35.75 with 7% bonus ($2.50) will give you $38.25 which equals 17 fares with nothing left over. The same apples to $37.85. The 7% bonus ($2.65) will give you $40.50 which covers 18 fares with nothing left over. One more: $39.95 with the 7% bonus ($2.80) will equal $42.75 which covers 19 fares with nothing left over.

What I have been doing lately is buying a $20.00 card (with bonus = $21.40) and adding $1.10 to it to make $22.50 for 10 fares (or when I am at the Transit Museum store buying a $21.03 card which with bonus equals $22.50).

BTW - on the old 15% bonus the minimum was $15.65 which with the bonus equaled $18.00 which covered 8 fares with nothing left over.


[To be on the safe side - I verifed my spreadsheet work here: http://www.metrocardbonuscalculator.com/]

I figured out the same thing on my spreadsheet but
I had a few attempts to purchase a card for anything but "whole dollars" rejected by the veding machine. I must admit I didn't specifically try 35.75 or 37.85 --- perhaps the machines are "programmed" to accept those specific amounts. Your experience with the Transit Museum store is interesting . . .

The MVMs will not accept anything but multiples of 5 cents (I have put 25 cents on a card I found that had $1.70 still on it). The minimum amount the machine will accept when using a debit/credit card is $2.25 (I am verifying this with the MTA but I did try to put $1.10 on a card using a debit card and the machine would nto accept the transaction.

[TCurtin]

Thsnks for your input guys. As I stated earlier my days for worrying about this are limited as I will become eligible for a senior "easy pay" card in August.

Tom

[railfan365]

The MVM's only take whole dollar amounts.Theoretically, someone could by a card with an exact number of rides by putting in $225 and getting 107 rides - but the maximum amount on a card at any on etime is $100 - which makes it impossible to have a card that worth an exact number of rides at all times.

HOWEVER, for someone like me who lives in New York and uses the local transport on an ongoing basis, it doesn't pay to worry about that since there will always be a balance on the card anyway (and the balance on an expiring card can be rolled over into a new one). At the same time, I don't want to have an odd fractin that will be difficult to resolve. What I'll be doin is putting in $45.00 at a time, and having an exact number after every fifth purchase. The rest of the time,the odd amount will be easily reslved eventually.

[Allan]

The MVM's only take whole dollar amounts.Theoretically, someone could by a card with an exact number of rides by putting in $225 and getting 107 rides - but the maximum amount on a card at any on etime is $100 - which makes it impossible to have a card that worth an exact number of rides at all times.

HOWEVER, for someone like me who lives in New York and uses the local transport on an ongoing basis, it doesn't pay to worry about that since there will always be a balance on the card anyway (and the balance on an expiring card can be rolled over into a new one). At the same time, I don't want to have an odd fractin that will be difficult to resolve. What I'll be doin is putting in $45.00 at a time, and having an exact number after every fifth purchase. The rest of the time,the odd amount will be easily reslved eventually.

The MVM's will take amounts in 5¢ increments (I have put 55¢ on a card and put in the exact amount in coins). Before they cut the bonus I used to buy a card from the MVM for $15.65 (total with bonus was $18.00). The minimum the machine will allow for a credit/debit transaction is $2.25 but for a cash transaction it accept as low as 5¢.

Instead of putting on $45.00 and having the fractions left over try this:

Put $35.75 on, you'll get a bonus of $2.50 for a total of $38.25 which is equal to 17 fares with nothing left over
Put $37.85 on, you'll get a bonus of $2.65 for a total of $40.50 which is equal to 18 rides with nothing left over
Put $39.95 on, you'll get a bonus of $2.80 for a total of $42.75 which is equal to 19 rides with nothing left over.

I'd go with the $37.85, that way you'll get 18 fares with nothing left over and you don't have to worry about that single odd fare (as in the 17 or 19 fare options).

[railfan365]

Thanks for the pointer Allan. Today, I had the first occasion since we last posted to add to my Metro Card and I got to see for myself that a purchase doesn't hav eto be in whole dollars. My card is now worth an even number of fares, and it will be easy to keep it that way.