Answer:
73 years
Explanation:
We can solve this problem by using the formula for the annually compounded interest:
[tex]A=P(1+r)^t[/tex]
where
A is the amount after time t
P is the principal
r is the interest rate
t is the time
In this problem, we have:
P = $2000 is the principal
r = 0.055 is the interest rate (equivalent to 5.5%)
We want to find the time t at which the amount invested will become
A = $100,000
Substituting these values into the formula and re-arranging it to make t the subject, we find:
[tex]t=log_{1+r}(\frac{A}{P})=log_{1.055}(\frac{100,000}{2000})\sim 73[/tex]
Therefore, the time taken is 73 years.
