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# [Smart Math] Percentages Problem 17

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

### Problem

What is the compound interest on $4000 for 1 year @ 5% per annum payable half-yearly? 1.$101.25
2. $200 3.$202.50
4. $400 5.$405

### The Usual Method

Rate of interest = 5% per annum

Hence, half-yearly rate of interest = $\frac{5}{2}=2.5$% per annum

Number of half years in1 year = 2

Hence, compound interest earned = $4000\left( 1+\frac{2.5}{100} \right)^{2}-4000=202.50$

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

5% of $4000 =$200
Hence, in this case, the actual interest earned will be slightly more than $200, i.e$202.50