Question of The Day07-12-2020

A sum of ₹ 3200 amounts to ₹ 5000 in 2 years at r% of interest per annuum compounded annually. What will be the amount that sum yields in 1-year time period, if it is invested at the same rate of interest per annum compounded 6-monthly?

Correct Answer : d ) ₹ 4050

Explanation :

We know, that compound interest is the concept of interest on interest

For r rate of interest compounded annually ratio of amount and principal for first year will be (100 + r) : 100, while this ratio changes to (100 + r)2 : 1002 in second year and so on

Now, according to the question

$${({{100+r}\over 100})^2}={5000 \over 3200}$$

⇒1$${100+r \over 100}=\sqrt{25 \over 16}={5\over 4}$$

⇒ 400 + 4r = 500

⇒ r = 25 %

Now, if rate of interest start compounding half yearly, then time period will be considered as 2 cycles of 6 months each

Then, Rate of interest for 6 months will be (r’) = 25/2 = 12.5%

Now, again the ratio of amount and principal will be (100 + r’)2 : 1002

Thus,

$${({{100+r'}\over 100})^2}={X \over 3200}$$

$${({{100+12.5}\over 100})^2}={X \over 3200}$$

$${{{81}\over 64}}={X \over 3200}$$

⇒ X = ₹ 4050

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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