Answer:
Rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.
Explanation:
Given that Cooper invested $ 3,100 in an account paying an interest rate of 2% compounded quarterly, while Robert invested $ 3,100 in an account paying an interest rate of 3% compounded continuously, to determine, after 12 years, how much more money would Robert have in his account than Cooper to the nearest dollar, the following calculation must be made:
Compound interest formula: Initial x (1 + interest / composition) ^ composition x years
Continuous compound interest formula: Initial x exp ^ (interest x years)
Cooper:
3,100 x (1 + 0.02 / 4) ^ 12x4 = X
3,100 x (1 + 0.005) ^ 48 = X
3,100 x 1,005 ^ 48 = X
3,100 x 1,270 = X
3,938.51 = X
Robert:
3,100 x 2.71828182845904 ^ (3x12) = X
4,443.32 = X
4,443.32 - 3,938.51 = X
504.51 = X
Therefore, rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.