Savings are assessed for SWA claims as follows:
First 5000 disregarded
Next 10000 assessed at 1 euro per 1000
Next 25000 assessed at 2 euro per 1000
Remainder assessed at 4 euro per 1000
In your case the assessment is:
First 5000 disregarded
Next 10000 assessed as 10 euro means
Remainder (20000) assessed as 20 euro means
Your total means from savings is currently 30 euro per week.
Single person households are required to pay a minimum contribution of 30 euro per week towards rent, plus any income in excess of the SWA rate (currently 186 euro pw).
In your case this is 30 (min contribution) + 2 (income above SWA) + 30 (means) = 62 pw.
Your weekly rent is 300 x 12 / 52 = 69.23 per week.
Entitlement to Rent Supplement is the weekly rent minus the amount you are expected to pay: 69.23 - 62 = 7.23 per week.
If your savings are reduced, your means will also reduce and your entitlement will increase.
You haven't specified which SW payment you are on - I'm guessing Illness Benefit or Disability Allowance from the 188 rate you mentioned. If you have not already applied, you should apply for Invalidity Pension, which is based on your PRSI contributions and a medical assessment. The rate of payment is slightly higher, and there are additional benefits such as the household benefits package which will help with electricity/gas, telephone and TV licence which you may qualify for.
You can get information on Invalidity Pension here:
http://www.welfare.ie/EN/Publications/SW44/Pages/1WhatisInvalidityPension.aspx