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# [Smart Math] Percentages Problem 3

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

### Problem

$2000 @ 5% compound interest after 4 years will become…? 1.$2235
2. $2378 3.$2431
4. $2586 5.$2601

The Usual Method:

New Principal = $P(1+r)^{n}$

i.e. $2000\times (1+0.05)^{4}$

= $2000(1.05)^{4}$

= 2000 x 1.2155

= $2431 (Ans: 3) Estimated Time to arrive at the answer = 75 seconds. Using Technique [contentblock id=google-adsense-post] Simply find the simple interest over 4 years as follows: 0.05 x 4 x 2000 = 400 Hence the new principal becomes 2000 + 400 = 2400. We also know that Compound Interest in this case will be > Simple Interest and also since the rate of interest is just 5% for only 4 years, the interest difference between Compound and Simple will not be ‘large’. Hence, the answer should be greater than$2400 but close to it. The only option that satisfies this condition is \$2431. Hence answer is option ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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