After 6 months, $1.78 simple interest was earned on an investment of $890. what was the annual interest rate

First you have to double the simple interest to get the amount earned in 1 year. That gives $3.56 earned and a total balance of $893.56
r = (1/t)(A/P - 1)  t=time, A=amount of money with interest, P=amount invested
r = (1/1)((893.56/890) - 1) = 0.004
r = 0.004
 now convert to a decimal to get .04 = 4%