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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

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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

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5% of $4000 =$200

Remember that whenever in Compound interest, whenever if the interest rate is halved but compounded twice, the net effect will always be slightly more than if the rate was taken as it is for 1 year.

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

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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