A sum of money would double itself in 10 years. The number of years it would be four times is:
To find the number of years it would take for the money to quadruple (become four times), we can use the concept of compound interest.
Let's assume the initial sum of money is P.
Given that the money will double itself in 10 years, we can write the equation:
P * (1 + r)^10 = 2P
where r is the annual interest rate.
Simplifying the equation, we get:
(1 + r)^10 = 2
To find the number of years it would take for the money to quadruple, we need to solve the equation:
P * (1 + r)^n = 4P
where n is the number of years.
Simplifying the equation, we get:
(1 + r)^n = 4
Now, we can compare the two equations:
(1 + r)^10 = 2 and (1 + r)^n = 4
Taking the log of both sides of the second equation will help us solve for n:
log((1 + r)^n) = log(4)
Using the property of logarithms, we can bring the exponent down:
n * log(1 + r) = log(4)
Now, we need to isolate the variable n:
n = log(4) / log(1 + r)
Approximating the value of r doesn't provide enough information, so we cannot calculate the exact value of n. However, this formula can be used to find the years it would take for the money to quadruple given any interest rate.