Here’s and example of a **SMART MATH** problem for **PERCENTAGES.**

**Problem**

**Problem**

$7500 is invested at 5% compound interest for 2 years. What is the interest in the 2^{nd} year?

- $293.75
- $375.75
- $393.75
- $400.75
- $468.75

**The Usual Method**

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Interest earned in the 1^{st} year = 5% of $7500

= 0.05 x 7500 = $375

Interest earned in the 2^{nd} 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 2^{nd} 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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