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Re: Amy deposited $1,000 into an account that earns 8% annual in
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12 Aug 2018, 05:02
Explanation
Both 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 $1,000×1.04=$1,040.00 (one interest payment at 4%) and Bob has $1,000×(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 $1,000×1.02=$1,020.00. After 6 months, Bob will have $1,020×1.02=$1,040.40.