# A person deposits a certain amount of money at the interest rate of 20% per annum compounded twice a year. If the person gets Rs. 302.50 after 1 year, then what will be the amount he invested in the starting?

2019-08-27 | Team PendulumEdu

**Options:**

**A**.** **Rs. 294

**B**.** **Rs. 240

**C**.** **Rs. 250

**D**. Rs. 280

**Solution:**

Amount (A) obtained on a principal amount (P), which is subjected to a compound interest rate (R) for a time period of (T) is given as

Given

Rate (R) = 20% per annum compounded twice a year

Time (T) = 1 year

Amount = Rs. 302.5

Let the principal amount he/she invested in the staring be Rs. P

For Periodic compounding within a year

Effective rate is taken as **(1/n) ^{th} ** times of rate given and effective time is taken as n

^{th}times of the time period given

Rate of interest compounded twice a year means Rate of interest compounded half yearly

So, Effective rate = 20/2 = 10%

And, Effective time period = 2*1 = 2

Now, Actual amount obtained because of compounding will be

P = 2.5*100 = Rs. 250

Hence, **(C)** is the correct answer.

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