To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = the amount of money after t years P = the initial principal (the sum of money) r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = the time in years
We know that the sum of money doubles in 3 years, so we can set up the following equation:
2P = P(1 + r/1)^(1*3)
Simplifying this equation, we get:
2 = (1 + r)^3
Taking the cube root of both sides, we get:
1 + r = 1.2599
r = 0.2599 or 25.99%
Now we need to find out how long it will take for the sum of money to become 4 times itself. Let’s call this time t. Then we have:
4P = P(1 + r/1)^(1*t)
Simplifying this equation, we get:
4 = (1 + r)^t
Taking the logarithm of both sides (with base 10, for example), we get:
log(4) = t*log(1 + r)
Solving for t, we get:
t = log(4) / log(1 + r)
Plugging in the value of r we found earlier, we get:
t = log(4) / log(1.2599)
Using a calculator, we find:
t ≈ 9.06
Therefore, it will take about 9.06 years for the sum of money to become 4 times itself at compound interest, compounded annually.