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# [Smart Math] Percentages Problem 1

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

### Problem

How much will $12,000 amount to in 2 years at compound interest if the rates for the 2 years are 5% and 7% per annum? 1.$12,662
2. $15,248 3.$14,336
4. $13,884 5.$13,482

### The Usual Method

Original Principle = $12,000 Principle after 1st year = 12,000 x 1.05 =$12,600
Principle after 2nd year = 12,600 x 1.07 = \$13,482

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds

### Using Technique

105 x 107 = 11235 (using Mental Math technique discussed in Multiplication Shortcuts
Now, 12,000 x 1.1235 is approximately equal to a 12 % increase in 12,000
i.e. $\frac{12000\times 12}{100}$ = 1440
Hence, the new Principle = 12,000 + 1440 = 13,440
However, this is an approximate answer. The real answer will be slightly greater than 13,440 (since, 1.1235 > 1.12). Thus looking at the options the answer is Rs, 13,482 – option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds
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