Respuesta :
Answer:
Dale will reach his goal at an annual rate of 11.83%.
Step-by-step explanation:
The formula for continuos compounding is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which A is the amount after t years, P is the principal(initial amount) and r is the annual rate.
Dale has 2000 dollars to invest.
This means that [tex]P = 2000[/tex]
He has a goal to have 5800 in this invest ment in 9 years.
So [tex]A(9) = 5800[/tex]
At what annual rate compounded continuously will Dale reach his goal?
This is r.
[tex]A(t) = Pe^{rt}[/tex]
[tex]5800 = 2000e^{9r}[/tex]
[tex]e^{9r} = \frac{58}{20}[/tex]
[tex]e^{9r} = 2.9[/tex]
[tex]\ln{e^{9r}} = \ln{2.9}[/tex]
[tex]9r = \ln{2.9}[/tex]
[tex]r = \frac{\ln{2.9}}{9}[/tex]
[tex]r = 0.1183[/tex]
Dale will reach his goal at an annual rate of 11.83%.
Answer:
Annual rate of 12.56%
Step-by-step explanation:
To find the annual rate, we need to use the compound interest formula:
M = Mo * (1+r)^t
where M is the goal value (M = 5800), Mo is the inicial value (Mo = 2000), r is the annual rate we want to find, and t is the number of years (t = 9). Then we can calculate the equation to find the value of r:
5800 = 2000 * (1+r)^9
(1+r)^9 = 5800/2000 = 2.9
1+r = 1.1256
r = 0.1256 = 12.56%
