A sum of money invested at compound interest doubles itself in six years. In how many years will it become 64 times itself at the same rate of compound interest?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 36
When interest is compounded, Amount $A = P (1 + \frac{R}{100})^{n}$
Given, $2 P = P (1 + \frac{R}{100})^{6}$
$=> 2 = (1 + \frac{R}{100})^{6}$ --- (1)
And, $64 P = P (1 + \frac{R}{100})^{n}$
$=> 64 = (1 + \frac{R}{100})^{n}$
$=> 2^{6} = (1 + \frac{R}{100})^{n}$
From eqn 1
$=> ((1 + \frac{R}{100})^{6})^{6} = (1 + \frac{R}{100})^{n}$
$=> (1 + \frac{R}{100})^{36} = (1 + \frac{R}{100})^{n}$
$=> n = 36$

Suggest Corrections

Similar questions

Q. A sum of money double itself in 4 years at compound interest. In how many years it will become eight times at same rate of interest

Q. Q. A sum of money doubles in 5 years at annual compound interest. Then in how many years will this sum of money become 8 times itself at the same rate of Interest Compounded annually?

A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?

Q. A sum of money under compound interest doubles itself in 4 years. In how many years will it become 16 times itself?

A sum of money doubles itself in $3$ years at compound interest, when the interest is compounded annually.In how many years will the sum amount to $16$ times of itself?

Join BYJU'S Learning Program

A sum of money invested at compound interest doubles itself in six years. In how many years will it become 64 times itself at the same rate of compound interest?

The correct option is B 36When interest is compounded, Amount A=P(1+R100)nGiven, 2P=P(1+R100)6=>2=(1+R100)6 --- (1)And, 64P=P(1+R100)n=>64=(1+R100)n =>26=(1+R100)n From eqn 1=>((1+R100)6)6=(1+R100)n =>(1+R100)36=(1+R100)n =>n=36