48 years will it become 16 times Option 3 is the right choice.
The sum of money doubles at compound interest in 6 years. In how many years will it become 16 times? Let's denote the principal amount as P.
If the principal amount doubles in 6 years, then after 6 years, it will be worth 2P. If it becomes 16 times the original amount after a certain number of years, then it will be worth 16P.
We can set up an equation to represent this situation:
16P = 2P(1 + r/100)^n
where r is the annual interest rate and n is the number of years.
Dividing both sides by 2P, we get:
8 = (1 + r/100)^n
Taking the natural logarithm of both sides, we get:
ln 8 = n ln(1 + r/100)
Solving for n, we get:
n = (ln 8) / (ln(1 + r/100))
We know that the principal amount doubles in 6 years, so we can plug in r = 100/6 and P = 1:
n = (ln 8) / (ln(1 + 100/600)) ≈ 48.08
Since we're dealing with time, we round up to the nearest whole year, so the answer is 48 years. Option 3 is the right choice.
Question:-
The sum of money doubles at compound interest in 6 years. In how many years will it become 16 times?
1. 16 years
2. 24 years
3. 48 years
4. 96 years