Final answer:
It takes approximately 8 years for $1400 to double at a 9% annual compound interest rate.
Step-by-step explanation:
To find out how long it takes for $1400 to double when invested at 9% compounded annually, we can use the formula for compound interest: 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 (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Since we want the principal to double, A is $2800 (which is $1400 x 2), P is $1400, r is 0.09 (9% as a decimal), and n is 1 since it is compounded annually. Plugging the values into the formula:
$2800 = $1400(1 + 0.09/1)^{1t}
We can simplify this to
2 = (1 + 0.09)^t
Using logarithms to solve for t:
log(2) = t * log(1.09)
t = log(2) / log(1.09)
After calculating, we get:
t = 8.0432 years
So, it will take approximately 8 years for $1400 to double at a 9% annual compound interest rate.