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
b. By what percent does the value of T(t) grow each year? Explain by writing a recursive formula for the
sequence T(1), T(2), T(3), etc.

Answer 1

6%

Explanation:

First, you need to know how to calculate the increase percentage of one quantity relative to another quantity. You need to use the following expression:

`Percent.increase= (new - original )/(original)(100)`

For example, if a group of 50 students increased to 60 students from 2018 to 2019, what is the percentage increase of the number of students?
`percent.increase=(60-50)/(50)(100)=20 percent`

In order to calculate the percentage increase each year with the values of the recursive formula, we have to calculate T(1), T(2) and T(3):

`T(1) = 1000(1.06)^(1)=1060\\T(2) = 1000(1.06)^(2)=1123.6\\ T(3) = 1000(1.06)^(3)=1191.016\\`

Now, the questions are: what is the increase percentage from T(1) to T(2) and from T(2) to T(3) (note that these results must be the same). Let's do the math:

`increase.percent=(T(2)-T(1))/(T(1))(100)=(1123.6-1060)/(1060)(100)=6 percent\\increase.percent=(T(3)-T(3))/(T(2))(100)=(1191.016-1123.6)/(1123.6)(100)=6 percent`

In conclusion, T(t) increases 6% each year.