The simple interest formula is A = P(1 + rt) in which A is the total of money after interest, P is your principal (starting) amount, r is the interest rate, and t is the amount of time. 
For 1), plug in your variables to get  A = 1500(1 + (7/100*1.5)). Simplify, and you’ll get A = 1500*1.105, and finally your answer, $1,657.50.

For 2), add your interest and principal amount, then plug in your variables to get 676 = 520(1 + 5r). Distribute to get 676 = 520 + 2600r. Subtract 520 from 676 to get 156 = 2600r, then divide both sides by 2600 to get a rate of 0.06, or 6%. 

For 3), add your interest and principal amount, then plug in your variables to get 1599 = 1300(1 + 5.75t). Distribute to get 1599 = 1300 + 7475t. Subtract 1300 from both sides to get 299 = 7475t, and then divide both sides by 7475 to get .04 = t, or a time period of four years. 

The other two problems can be solved using the formula and steps described above. If you still need help with them, leave a comment and I will solve those as well.