A sum of money becomes eight times in 3 years, it the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?Options6 years8 yearsNone of these5 years4 years

The problem is about compound interest.

Given that a sum of money becomes eight times in 3 years, we can use the formula for compound interest to find the rate. The formula is:

A = P(1 + r/n)^(nt)

Where: A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money) r is the annual interest rate (in decimal) n is the number of times that interest is compounded per year t is the time the money is invested for in years

In this case, A is eight times the initial amount, P is the initial amount, n is 1 (since the interest is compounded annually), and t is 3 years. We can set up the equation as follows:

8P = P(1 + r/1)^(1*3)

Solving for r, we get r = 2 (or 200%).

Now, we want to find out how long it will take for the same amount of money to become sixteen times at the same compound rate. We can set up a similar equation:

16P = P(1 + 2/1)^(1*t)

Solving for t, we get t = 4 years.

So, the same amount at the same compound rate will become sixteen times in 4 years. Therefore, the answer is 4 years.