Question 94

An unknown sum when compounded annually yields extra interest that is equal to 2401 times of the unknown sum compared to simple interest. If the unknown sum, rate of interest r% and time 2 years is same for compound and simple interest, then find the value of the expression $$\sqrt{50(r + 1)}$$.

Solution

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Let us assume the unknown sum to be P.
Compound interest for 2 years = $$P\left(1+r\right)^2$$ and simple interest for 2 years = $$2\Pr$$.
The difference between them is equal to $$2401\times\ P$$.
This gives: $$P\left(1+r\right)^2-2\Pr=2401\times\ P$$ 
==> $$\left(1+r\right)^2-2r=2401$$. After opening the square, we get $$r^2=2401$$ or r = 49.
50(r+1) = 2500 and it's root will be 50 i.e. Option D.

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