How long will it take $7,000 invested at 5.5% compounded daily to grow to $14,000? Round your answer to the nearest tenth of a year.

To find out how long it will take for $7,000 to grow to $14,000 at an interest rate of 5.5% compounded daily, we can use the formula for compound interest:

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

Where:
A = the final amount (in this case, $14,000)
P = the principal amount (in this case, $7,000)
r = the annual interest rate (in decimal form, so 5.5% becomes 0.055)
n = the number of times interest is compounded per year (in this case, daily compounding, so n = 365)
t = the number of years

Now we can plug in the given values into the formula and solve for t:

$14,000 = $7,000(1 + 0.055/365)^(365t)

Divide both sides of the equation by $7,000:

2 = (1 + 0.055/365)^(365t)

Take the natural logarithm (ln) of both sides of the equation:

ln(2) = 365t * ln(1 + 0.055/365)

Divide both sides of the equation by 365 * ln(1 + 0.055/365):

t = ln(2) / (365 * ln(1 + 0.055/365))

Now, we can calculate t by substituting the values into the formula:

t = ln(2) / (365 * ln(1 + 0.055/365))
t ≈ 12.7 years

Therefore, it will take approximately 12.7 years for the investment to grow from $7,000 to $14,000 at an interest rate of 5.5% compounded daily.