Question : A sum is deposited in a bank which gives simple interest. The sum becomes 1.25 times in 3 years. If there is a requirement of INR 7,60,000 after seven years, how much amount (in INR) should one deposit to fulfil the requirement?
Option 1: 5,20,000
Option 2: 5,70,000
Option 3: 4,80,000
Option 4: 6,00,000
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Correct Answer: 4,80,000
Solution :
The sum becomes 1.25 times in 3 years
Let the deposit be $P$
⇒ Interest earned $= 1.25P - P = 0.25P$
According to the formula
Simple interest $=\frac{P\times r\times t}{100}$
⇒ $0.25P =\frac{P\times r ×3}{100}$
⇒ $r=\frac{100\times 0.25P}{P\times3}$
⇒ $r = \frac{25}{3}$%
There is a requirement of INR 7,60,000 after seven years,
So, Interest earned $= 760000 - P$
Again, the simple interest $=\frac{P\times r\times t}{100}$
⇒ $760000 - P = \frac{P×\frac{25}{3}×7}{100}$
⇒ $\frac{7P}{12} + P = 760000$
⇒ $\frac{19P}{12} = 760000$
⇒ $P = 760000×\frac{12}{19}$
⇒ P = INR 4,80,000
Hence, the correct answer is 4,80,000.
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