Question 1135947
if the investment is doubled, then it will be equal to 20,000.


formula is f = p * (1 + r) ^ n


f is the future value
p is the present value 
r is the interest rate per time period.
n is the number of time periods.


the time periods are in years.


f = 20,000
p = 10,000
r = 8% / 100 = .08


formula becomes 20,000 = 10,000 * (1 + .08) ^ n


simplify to get 20,000 = 10,000 * 1.08 ^ n


divide both sides of this equation by 10,000 to get 20,000 / 10,000 = 1.08 ^ n.


simplify to get 2 = 1.08 ^ n.


take the log of both sides of this equation to get log(2) = log(1.08 ^ n)


since since log(1.08 ^ n) = n * log(1.08), the equation becomes:


log(2) = n * log(1.08).


divide both sides of this equation by log(1.08) to get:


log(2) / log(1.08) = n


solve for n to get n = 9.006468342


10,000 * 1.08 ^ 9.006468342 = 20,000, confirming the solution is correct.


your solution is that the investment will double in 9.006468342 years.