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A certain amount is kept in a bank at 8% compound interest. An equal amount is kept in another bank at 10% simple interest. When the amount in the first bank gets doubled, by what percentage does the amount with the second bank increase? log 102 = 0.3 & log101.08 = 0.033 
  • a)
    60%
  • b)
    70%
  • c)
    80%
  • d)
    90%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A certain amount is kept in a bank at 8% compound interest. An equal a...
Solution: Let the amount kept with the 1st bank be P. Thus, the amount kept with the 2nd bank is also P.
Now, we have 
Or 2 = 1.08n
Taking log on both the sides, we get, log10 2 = log10 1.08n
log10 2 = n log10 1.08
∴ n = 0.3/0.033 ≌ 9
The amount gets doubled in 9 years.
Now, simple interest for 9 years is 
Thus, increase % = 90%
Hence, option 4.
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Most Upvoted Answer
A certain amount is kept in a bank at 8% compound interest. An equal a...
Let's assume the initial amount kept in both banks is x.

After a certain period of time, the amount in the first bank becomes 2x.

Using the compound interest formula, we can write the equation as:

2x = x(1+8/100)^n

Simplifying the equation, we get:

2 = (1.08)^n

Taking the logarithm of both sides, we have:

log 2 = n*log(1.08)

Dividing both sides by log(1.08), we get:

n = log 2 / log(1.08)

n ≈ 9.006

Therefore, the amount in the first bank doubles after approximately 9 years.

Now, let's calculate the interest earned in the second bank over the same period of time using simple interest:

Interest = Principal * Rate * Time
= x * (10/100) * 9
= 0.9x

So, the amount in the second bank after 9 years is x + 0.9x = 1.9x.

The increase in the amount with the second bank is:

Increase = (1.9x - x) / x * 100%
= 0.9x / x * 100%
= 90%

Therefore, the amount with the second bank increases by 90%.
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