Surrendering Life Insurance as gift

My grandmother gave me as a gift when I was a baby a $10,000 life insurance policy that would be paid up once I turned 30. Now the policy is worth just over $11,000. I have turned 30 and I am looking to cash the policy out to possibly use on other investments. Since she is still the owner she would have to pay the taxes, but we don't know on what portion she would have to pay the taxes. Is it the $1,100 or the total cash amount in which she would have to pay the taxes on? Also since it was a gift would she have to pay any taxes at all. Any help is appreciated. Thanks.

She would have to pay taxes on the amount you cashed out less the amount paid in. When she gives you the $11,000 she can do it tax free as a gift.

-Joe

Do state and local taxes have to be paid if this policy is paid out?

Further information on the policy.
Cost of policy $5k
Once I turned 30 on July 26 the policy would be worth $10K.
The cash value is just over $11K.
What would the taxable amount be?

The taxable amount as you stated would be $6000, taxed at normal income. This is the cash value $11k - the cost basis $5k.