NYC Metro card computations

As I work from home I don't need monthly metro card.  (Although I may buy one in the winter to encourage myself to leave the house more often, to prevent SAD attacks).  I just buy a $10 card every once in a while and add more as I need it.  

but...

I often find myself trying to calculate if this is the most effective way of spending. So this time I am going to do my computations online for my benefit and anyone else who is trying to figure this out. 

My rough estimate is: I should buy a 7 day unlimited if I am going to go on one (roundtrip, in other words two trips) trip to Manhattan for 6 out of the next 7 days.   Lets see how that estimate holds up:

7-day-unlimited = $27

MTA

$27 divided by $2.25 (the cost of a single ride) = 12 rides

So one 7-day-unlimited equals 12 singles rides.

.....except....

that when you put money on an unlimited ride card you get a 15% bonus, 

so, lets see 12 rides is $27 dollars worth, but if you figure out the bonuses

To get $27 we make $27=115% and make x=100% and put $27 over x  = 115 over 100 (how in the world do I show this better on the blog, ugh!)

So that means 115x=2700, and we divide both side by 115 to solve for x.

so x equals $23.48

(Double check the math $23.48 time 15% is $3.52. $23.48 plus $3.52 equals  $27.00  Yes!!)

SO really a 7-day-unlimited is not equivalent to 12 single rides (or 6 days of going in and out) 

If you put $27 on a pay-per-ride card you would get $31.50 (including you 15% bonus) or 13.8 rides. 

Conclusion a 7-day-unlimited is good if you are going into and out of the city 7 out of 7 days or more (14 trips or more). 

So for me in and out tonight, in and out tomorrow, in and out Saturday, and maybe Thursday,  that's 8 rides, that's not worth it. 

(ps, this site says: If you ride at least 46 times a month, you should get an unlimited card.)