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Q.

If the amount on the principal of Rs.6000 is written as 6000 1+ 5 100 3   and compound interest payable for 6 months, then the rate of interest p.a. is ____ % and time is ____ years.


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Detailed Solution

If the amount on the principal of Rs.6000 is written as 6000 1+ 5 100 3   and compound interest payable for 6 months, then the rate of interest p.a. is 10 % and the time is 1.5 years.
It is given that the amount on the principal of Rs.6000 is 6000 1+ 5 100 3 .  
We know that,
If the interest is compounded for 6 months, then
  C.I.=P 1+ R 200 2t −P  
And, the total amount s given by,
Amount = Principal Amount + C.I.
Therefore we have,
Amount=6000 1+ 5 100 3         ...(1)   Since the interest is compounded for 6 months, then
  C.I.=P 1+ R 200 2t −P  
It is given that the principal amount = Rs.6000.
⇒Amount=6000+6000 1+ R 200 2t −6000   ⇒Amount=6000 1+ R 200 2t       ....(2)   From equations (1) and (2), we get,  6000 1+ R 200 2t =6000 1+ 5 100 × 2 2 3     ⇒6000 1+ R 200 2t =6000 1+ 10 200 3   By comparing both the sides, we will get  2t=3 and R = 10.  
   ∵2t=3 ⇒t= 3 2 =1.5   Therefore the rate of interest per annum is 10% and the time is 1.5 years.
 
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