Answer:
73 years
Explanation:
To solve this problem, we can use the formula for the annual compound interest, which is:
[tex]A=P(1+r)^t[/tex]
where:
A is the final amount after time t
P is the principal
r is the rate of interest
t is the time
In this problem, we have:
[tex]P=\$2000[/tex] is the principal
[tex]r=0.055[/tex] is the interest rate (5.5%)
We want to find the time t at which the amount of money is
A = $100,000
Therefore, we can re-arrange the equation and solve for t:
[tex](1+r)^t=\frac{A}{P}\\t=log_{1+r}(\frac{A}{P})=log_{1+0.055}(\frac{100,000}{2000})=73[/tex]
So, it will take 73 years.
