Question

The annual interest rate for Jack's savings account increased from 2.1% to 3.2%. Complete parts (a) and (b) below.a. Describe the change as an absolute change in terms of percentage pointsThe annual interest rate increased by percentage points.(Type an integer or decimal rounded to the nearest tenth as needed.)b. Describe the change as a relative change in terms of a percentageThe annual interest rate increased by %.(Type an integer or decimal rounded to the nearest tenth as needed.)

Answer 1

Step 1

Given;

`\begin{gathered} \text{Initial annual interest;2.1\%} \\ \text{Current annual interest=3.2\%} \end{gathered}`

Step 2

Describe the change as an absolute change in terms of percentage points. Absolute change is given as;

`\text{Current annual interest}-\text{Initial annual interest}`
`\begin{gathered} 3.2-2.1=1.1\text{ \%}^{} \\ \end{gathered}`

The annual interest rate increased by 1.1 percentage points.

Step 3

Describe the change as a relative change in terms of a percentage.

`Relative\text{ change in \%=}\frac{Absolute\text{ c}hange}{\text{initial annual interest}}*100`
`\begin{gathered} Relative\text{ change in \%=}(1.1)/(2.1)*100=52.38095 \\ Relative\text{ change in \%}\approx52.4 \end{gathered}`

The annual interest rate increased by 52.4 % to the nearest tenth.