Question

Dale has 2000 dollars to invest. He has a goal to have 5800 in this invest ment in 9 years. At what annual rate compounded continuously will Dale reach his goal?

Answer 1

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:

$A(t) = Pe^{rt}$

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 $P = 2000$

He has a goal to have 5800 in this invest ment in 9 years.

So $A(9) = 5800$

At what annual rate compounded continuously will Dale reach his goal?

This is r.

$A(t) = Pe^{rt}$

$5800 = 2000e^{9r}$

$e^{9r} = \frac{58}{20}$

$e^{9r} = 2.9$

$\ln{e^{9r}} = \ln{2.9}$

$9r = \ln{2.9}$

$r = \frac{\ln{2.9}}{9}$

$r = 0.1183$

Dale will reach his goal at an annual rate of 11.83%.

Answer 2

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%