Problem: on a certain day , tim invested $ 1,000 at 10 percent annual interest , compounded annually , and lana invested 2,000 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 ?
Rationale: "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 1,000 ( 1.10 ) ^ 2 = 1,000 ( 1.21 ) = 1,210 and lana would have 2,000 ( 1.05 ) ^ 2 = 2,000 ( 1.1025 ) = 2,205 thus , tim earned 210 dollars , while lana earned 205 dollars the difference is $ 5 and the answer is a ."
annotated_formula: subtract(subtract(multiply(1,000, power(add(const_1, divide(10, const_100)), 2)), 1,000), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 2,000), 2,000))