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? Choose one:
A) $ 5
B) $ 15
C) $ 50
D) $ 100
E) $ 105
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">1_000 * (121/100)</gadget>
<output>1_210</output>

<gadget id="calculator">1_210 - 1_000</gadget>
<output>210</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">(441/400) * 2_000</gadget>
<output>2_205</output>

<gadget id="calculator">2_205 - 2_000</gadget>
<output>205</output>

<gadget id="calculator">210 - 205</gadget>
<output>5</output>

<result>A</result>
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?
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))
"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 ."