Type the correct answer in the box. round your answer to the hundredth.
an investment in a savings account grows to three times the initial value after tyears.
if the rate of interest is 5%, compounded continuously, t =
i
y ears.

Approximately 22.97 years

Step-by-step explanation:

Use the equation for continuously compounded interest, which uses the exponential base "e":

Where P is the principal (initial amount of the deposit - unknown in our case)

A is the accrued value (value accumulated after interest is compounded), in our case it is not a given value but we know that it triples the original deposit (principal) so we write it as: 3 P (three times the principal)

k is the interest rate : 5% which translates into 0.05

and t is the time in the savings account to triple its value (what we need to find)

The formula becomes:

To solve for "t" we divide both sides of the equation by P (notice it cancels P everywhere), and then to solve for the exponent "t" we use the natural logarithm function:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2