1) initial investment = $600
annual % rate = ?
time to double = ?
amount after 10 years = $19,205.00
19,205 = 600e^(10r)
I do not know how to solve for r of find the time to double.
To solve for the annual percentage rate (r) or the time it takes for an investment to double, you will need to use logarithmic functions.
1) Solving for the annual percentage rate (r):
We have the equation: 19,205 = 600e^(10r)
To isolate "r," divide both sides of the equation by 600:
19,205 / 600 = e^(10r)
Now, take the natural logarithm (ln) of both sides of the equation to remove the exponential:
ln(19,205 / 600) = ln(e^(10r))
Using the property of logarithms that ln(e^x) = x, we can simplify:
ln(19,205 / 600) = 10r
Finally, divide the result by 10 to solve for "r":
r = ln(19,205 / 600) / 10
Use a scientific calculator or an online tool to calculate the natural logarithm and solve for the annual percentage rate (r).
2) Solving for the time to double:
We can also use logarithms to find the time it takes for an investment to double. The formula is:
time to double = ln(2) / r
Substitute the value of "r" we obtained in the previous step into the formula:
time to double = ln(2) / [ln(19,205 / 600) / 10]
Evaluate this expression using a calculator or an online tool to find the time it takes for the investment to double.