on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
"compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 105 dollars , while lana earned 82 dollars the difference is $ 23 and the answer is c ."
subtract(subtract(multiply(500, power(add(const_1, divide(10, const_100)), 2)), 500), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 800), 800))