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Percentages Smart Math

[Smart Math] Percentages Problem 3

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

Percentages

Problem

$2000 @ 5% compound interest after 4 years will become…?

  1. $2235
  2. $2378
  3. $2431
  4. $2586
  5. $2601


The Usual Method:

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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

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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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