Answer:
Approximately 22.97 years
Step-by-step explanation:
Use the equation for continuously compounded interest, which uses the exponential base "e":
[tex]A=P e^{k*t}[/tex]
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:
[tex]3P = P e^{0.05 * t}[/tex]
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:
[tex]\frac{3P}{P} = \frac{P}{P} e^{0.05 * t}[/tex]
[tex]3 = e^{0.05 * t}[/tex]
[tex]ln(3) = 0.05 * t[/tex]
[tex]t = \frac{ln(3)}{0.05} = 21.972245... years[/tex]
