The difference between simple and compound interest for the fourth year...

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The difference between simple and compound interest for the fourth year is Rs. 7280 at 20% p.a. What is the principal sum?

A. 10000

B. 50000

C. 70000

D. 40000

Answer: Option B

Solution(By Examveda Team)

Difference between Compound interest and Simple interest for the fourth year is Rs. 7280
$$\eqalign{ & P{\left( {\frac{6}{5}} \right)^3}\left( {\frac{1}{5}} \right) - \frac{P}{5} = 7280 \cr & \frac{P}{5}\left[ {{{\left( {\frac{6}{5}} \right)}^3} - 1} \right] = 7280 \cr & \frac{P}{5}\left[ {\frac{{216}}{{125}} - 1} \right] = 7280 \cr & \frac{P}{5} \times \frac{{91}}{{125}} = 7280 \cr & \therefore P = 50000 \cr} $$

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Comments ( 5 )

Athul RM :

4 years ago

Bro.. just find the CI for the 4 th year.. that is principal *(1.2^4-1.2^3)
Then SI for the 4 th year.. that is 0.2p
Now substract and equate
You will get 0.3456-0.2
Sanjib Kumar :

5 years ago

How is the formula originated? If anyone explains it....👏👏👏
Actually I want to know how (Pr/100) is got common...
JK Jk :

6 years ago

The answer is 50000,ok
But CI for 3 years =(50000*1.2*1.2*1.2) - 50000=86400-50000=36400
SI for 3 years =50000*3*20/100=30000
Difference between CI & SI =36400-30000=6400
If it for 4 years
CI for 4 years =(50000*1.2*1.2*1.2*1.2)-50000= 103680-50000=53680
SI for 4 years =50000*4*20/100=40000
Difference between CI & SI =53680-40000=13680
Both ways should get one answer, right?
Can anyone help Where I get wrong?
Prasanna Azhaganantham :

6 years ago

the difference is only for the 4th year not for a period of 4 years. the solution is correct.
Ajith Narayanan :

6 years ago

The answer is wrong, in fact the formula applied is wrong.
Try calculating the Compound interest and Simple interest with 50000 as principle for 4 years with 20 % per annum the difference between them is not 7280.