SATHEE: Quantitative Aptitude Ques 1808

Quantitative Aptitude Ques 1808

Question: A certain sum invested with interest of 8% per annum, compounded semi-annually amounts to Rs. 6760 at the end of 1 yr. The sum is

Options:

A) Rs. 6000

B) Rs. 6520

C) Rs. 6250

D) Rs. 6500

Show Answer

Answer:

Correct Answer: C

Solution:

Let the sum invested be Rs. x. Amount at the end of 1 yr = Rs. 6760 Now, rate of interest = 8% and time duration is 1 yr. Given, in the question that the amount is compounded semi-annually, i.e. half-yearly. Hence, rate of interest changes to $ \frac{R}{2}=\frac{8}{2} $ % =4% and time duration becomes $ 2t=2\times 1=2yr $ By the formula of compound interest, we get Amount $ =P{{( 1+\frac{R}{100} )}^{t}} $

$ \Rightarrow $ $ 6760=x{{( 1+\frac{4}{100} )}^{2}} $
$ \Rightarrow $ $ x=\frac{6760}{{{( 1+\frac{1}{25} )}^{2}}} $

$ \Rightarrow $ $ x=\frac{6760\times 25\times 25}{26\times 26}=10\times 25\times 25 $

$ \Rightarrow $ $ x=6250 $

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