Ram Lal invested a certain amount for three years, under compound interest compo

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Ram Lal invested a certain amount for three years, under compound interest compounded annually and received Rs.17820. If he had invested the same amount for six years at the same rate of interest compounded annually, he would have received Rs.49410. What amount (in Rs.) did he invest?

Answer: Option D
:
D
Let the sum be P and the interest rate be r.
Then after ‘n’ years

A = P (1 + \frac{r}{100})^{n} = P R^{n} w h e r e R = 1 + \frac{r}{100}

Now,

17820 = P R^{3}, 49410 = P R^{6}

R^{3} = \frac{49410}{17820}

So,

P = \frac{17820 \times 17820}{49410}

=Rs.6427

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