If a sum on compound interest (compounded yearly) becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:

16 years

We know ,

Amount = Principal × ( 1 + \(\frac{rate }{100}\) )^t

Let principal = P

3P = P × ( 1 + \(\frac{rate }{100}\) )⁴

3 =  ( 1 + \(\frac{rate }{100}\) )^{4   --------(1)}

Now,

After t years sum becomes 81 times of itself.

81P = P × ( 1 + \(\frac{rate }{100}\) )^t

34 = P × ( 1 + \(\frac{rate }{100}\) )^t

Using equation 1 ,

( 1 + \(\frac{rate }{100}\) )¹⁶ =   ( 1 + \(\frac{rate }{100}\) )^t

So , t = 16 years