Question

Tim deposits money in a certificate of deposit account. The balance (in dollars) in his account t years after making

the deposit is given by T(t) = 1000(1.06)t for t ≥ 0
a. Explain, in terms of the structure of the expression used to define T(t), why Tim’s balance can never be $999

Answer 1

The minimum balance is $ 1,000

Explanation:

According to the expression used to define the balance in Tim's account, at time t = 0:

`T(0) = 1000(1.06)^(0)\\T(0) = 1000(1)\\T(0)=1000`

Then, the initial balance in Tim's account is 1000 dollars. One year later, the balance in Tim's account will be:

`T(1)=1000(1.06)^(1)\\T(1) = 1060`

And each subsequent year, the balance will increase in a factor of 1.06. The minimum balance in Tim's account is 1000, and there is no possibility that the balance could be less than that amount of money.