ExplanationBoth Amy and Bob start with $1,000 and earn 8% interest annually; the difference is in how often this interest is compounded. Amy’s interest is compounded twice a year at 4% each time (8% annual interest compounded 2 times a year means that she gets half the interest, or 4%, every 6 months).

Bob’s interest is compounded four times a year at 2% (8% divided by 4 times per year) each time. After 6 months, Amy has \(\$1,000 \times 1.04 = \$1,040.00\) (one interest payment at 4%) and Bob has \(\$1,000 \times (1.02)^2 = $1,040.40\) (two interest payments at 2%). The difference is \(\$1,040.40 – \$1,040.00 = \$0.40\).

Alternatively, Bob’s interest could be calculated as two separate payments. After three months, Bob will have \(\$1,000 \times 1.02 = \$1,020.00\). After 6 months, Bob will have \(\$1,020 \times 1.02 = \$1,040.40\).

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Sandy

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