Here’s and example of a SMART MATH problem for PERCENTAGES.
Problem
$7500 is invested at 5% compound interest for 2 years. What is the interest in the 2nd year?
- $293.75
- $375.75
- $393.75
- $400.75
- $468.75
The Usual Method
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Interest earned in the 1st year = 5% of $7500
= 0.05 x 7500 = $375
Interest earned in the 2nd year = 5% of $7500 + 5% of $375
= (0.05 x 7500) + (0.05 x 375) = 375 + 18.75 = $393.75
(Ans: 3)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Interest earned in 2nd year has to be slightly larger than $375 (5% of $7500), since we have to add the interest accrued on the interest of the previous year. However, this additional amount being small (due to 5%), we can approximate the actual answer to a value slightly greater than $375, but close to it. The only options satisfying these conditions are ‘2’ and ‘3’. Option ‘2’ is eliminated as it is ‘too close to’ $375.
(Ans: 3)
Estimated Time to arrive at the answer = 5 seconds.
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