Part A:
Let B(t) be the amount of money in the account after t months with an initial deposit of $100.
Since the amount increases by 0.2% every month, the amount after t months can be found using the formula:
B(t) = 100 * (1 + 0.002)^t
Part B:
To find the factor by which the amount in the account increases every month, we need to calculate (1 + 0.002):
(1 + 0.002) ≈ 1.002
So the amount in the account increases by a factor of approximately 1.002 every month.
To find the factor by which the amount in the account increases every year, we need to calculate the factor for 12 months:
(1 + 0.002)^12 ≈ 1.026
So the amount in the account increases by a factor of approximately 1.026 every year.
To find the factor by which the amount in the account increases every 5 years, we need to calculate the factor for 60 months:
(1 + 0.002)^60 ≈ 1.136
So the amount in the account increases by a factor of approximately 1.136 every 5 years.