A sum of money is doubled in 7 years at the compound interest rate. In how many years it will be8 times its actual value

To solve this problem, we need to understand the concept of compound interest.

Given that the sum of money is doubled in 7 years, we can use the formula for compound interest:

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

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

In this case, the money is doubled, so A is 2P, and t is 7 years. We don't know the values of r and n, but we can say that the interest is compounded annually for simplicity, so n is 1.

So the equation is: 2P = P(1 + r)^7

Solving for r, we get r = (2^(1/7)) - 1

Now, we want to find out when the sum will be 8 times its actual value. So, A is now 8P. We use the same formula, but replace r with the value we found, and solve for t:

8P = P(1 + (2^(1/7) - 1))^t

Solving for t, we get t = log(8) / log(2^(1/7))

Calculating this, we get t approximately equal to 21 years.

So, the sum of money will be 8 times its actual value in approximately 21 years.