With taxes, card fee, etc., the default values of Metrocards (excluding unlimited rates), always result in small change remaining at the end of usage. In order to avoid this waste or hassle of refilling the remaining value, mathematics comes to play:
The key is to use the OTHER AMOUNTS feature (Thanks to MTA for being this considerate, at least).
Currently, with $2.50 per ride (I should revisit this entry and adjust the rates accordingly as MTA always raises the fee from time to time), the magic numbers are:
$11.90, $19.05 or $30.95
Now that the single ride rate is $2.75, 7-day = $31, 30-day = $116.50,
11% bonus (applies only to the new credit, not the total) for > $5.50, ignoring $1 card fee,
Here's the unverified table I come up for economic purchase value:
Based on their site, nickel increment is the smallest increment allowed.
Now we can just use http://enterprise.mtanyct.info/MetroCardCalculator/