Do I need to have 20 % down payment when I refinance from FHA loan to conforming ?

Hello everyone. I am purchasing a house but the loan I could get was FHA because i did not have 20 % down and not enough credit for conforming loan. I could put 15 % down on the house but my question is whether i should do that or go with the minimum of 3 % because with FHA loan you pay premium mortgage insurance 1.5 % upfront and .5 higher interest rate. Lets say if i build a better credit in 6 months to qualify for a conforming rate and refinance the house from FHA to conforming do i need to have 20 % down for conforming loan or should i put the money to FHA loan and that 15 % is counted as home equity. All I need is 5 % after that right or do i need to have 20 % in cash?

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