Question

The amount of money in a savings account increases by 0.2% every month.

Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.

Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:

Answer 1

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.