I am 25 Y/M. I had a hair transplant at 4/08/2015

Finasteride will not affect your transplanted hairs.  Finasteride will affect your non-transplanted hairs.  All drugs have side effects.  If you are concerned about taking the medication, speak with your doctor about it's risks and benefits.

Finasteride will not affect the transplanted hairs. The surgeon likely prescribed finasteride to you in order to prevent the hairs that are currently there from falling out. Potential side effects are possible albeit uncommon. Be sure to speak to your surgeon again if you are unsure of the short and long term plan for your hair.

Your doctor is smart because finasteride will prevent shock loss which happens in young men who are losing hair when they had a hair transplant. As the side effects only occur in one in fifty people, don't worry about it unless you develop the side effects. If you wait taking the medications, then the shock loss becomes a real risk in young men so i would not delay.