The answer is $1219
Interest = Total amount * interest rate * time ( I=prt is the formula for calculating interest)
In this case,
Total amount = $1200
Interest rate= $ 0.19
Time span for which interest rate is being calculated= 1/12 (since the rate is yearly and we are calculating interest for a month)
Interest = 1200*0.19*1/12 = 19
So the total amount owned by family at the end of one month = original amount + interest = $1200 + $19 = $1219