Answer:
It takes 22.52 years for the balance to triple in value.
Step-by-step explanation:
Continuous compounding:
The amount of money earned using continuous compounding is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount of money and r is the interest rate, as a decimal.
Interest rate of 5%.
This means that [tex]r = 0.05[/tex], and thus:
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = A(0)(1+0.05)^t[/tex]
[tex]A(t) = A(0)(1.05)^t[/tex]
Time for the balance to triple?
This is t for which [tex]A(t) = 3A(0)[/tex]. So
[tex]A(t) = A(0)(1.05)^t[/tex]
[tex]3A(0) = A(0)(1.05)^t[/tex]
[tex](1.05)^t = 3[/tex]
[tex]\log{(1.05)^t} = \log{3}[/tex]
[tex]t\log{1.05} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{\log{1.05}}[/tex]
[tex]t = 22.52[/tex]
It takes 22.52 years for the balance to triple in value.
