Question

Type the correct answer in the box. Round your answer to the hundredth.

Answer 1

Answer:

Approximately 22.97 years

Step-by-step explanation:

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

$A=P e^{k*t}$

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:

$3P = P e^{0.05 * t}$

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:

$\frac{3P}{P} = \frac{P}{P} e^{0.05 * t}$

$3 = e^{0.05 * t}$

$ln(3) = 0.05 * t$

$t = \frac{ln(3)}{0.05} = 21.972245... years$