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.
That looks like a misprint, but if the investment really increased that fast,
19,205 = 600 (1 + r)^10
10 ln (1+r) = ln (19,205/600) = ln 32.0
= 3.4657
ln (1+r) = 0.34657
1+r = 1.414
r = 41.4%
The time to double is 2.0 years
To solve for the annual percentage rate (r) and the time it takes to double your investment, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the final amount
P is the initial investment
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, we have the final amount A = $19,205, the initial investment P = $600, and the number of years t = 10. Since we are not given the value for n, we can assume it is compounded annually (n = 1).
Now, we can rewrite the equation as:
19,205 = 600 * (1 + r/1)^(1*10)
Simplifying it further:
19,205 = 600 * (1 + r)^10
To solve for r, we need to isolate it. Let's divide both sides of the equation by 600:
(1 + r)^10 = 19,205 / 600
Now, we can take the 10th root of both sides:
(1 + r) = (19,205 / 600)^(1/10)
Finally, subtracting 1 from both sides gives us the value of r:
r = (19,205 / 600)^(1/10) - 1
Using a calculator, you can simplify the right-hand side and find the value of r.
To find the time it takes to double your investment, you can use the rule of 72, which states that the time it takes to double an investment is approximately equal to 72 divided by the annual interest rate.
In this case, let's use the value of r that we just calculated. We can plug it into the formula:
Time to double = 72 / r
Calculate this expression, and you will get the time it takes to double your investment.