Answer: Rs 2500
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Explanation:
Compute the simple interest on a deposit of x
The per annum (p.a.) interest rate is r = 0.12 from the 12% value mentioned.
We do so over t = 2 years
i = p*r*t
i = x*0.12*2
i = 0.24x
Let A = 0.24x
Do the same for the compound interest. We'll have n = 1 to reflect annual compounding.
i = p*(1+r/n)^(n*t) - p
i = x*(1+0.12/1)^(1*2) - x
i = 1.2544x - x
i = 0.2544x
Let B = 0.2544x
We're told that "The simple interest on a sum of money in 2 years is Rs 36 less than the compound interest compounded annually"
This means the interest earned in the simple interest (value A) is Rs 36 less than the amount earned with quantity B
So,
A = B-36
0.24x = 0.2544x - 36
0.24x - 0.2544x = -36
-0.0144x = -36
x = -36/(-0.0144)
x = 2500
The amount invested or deposited is Rs 2500
