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:
Answer & explanation
Correct answer: option 4
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