Question

I need help with C, what’s the approximate annual growth rate of the ring? How does this result relate to your answer in part B?

Answer 1

`\begin{gathered} C.\text{ Annual interest rate of ring= 3.96\%} \\ \text{ It is greater than the necklace that's why the value increases more.} \end{gathered}`

Explanation:

It is given that the value of a necklace increases by 3.2% per year, then by the equation of future value, the value of the necklace after t years will be:

`\begin{gathered} A(n)=1(1+(3.2)/(100))^t \\ \text{ The initial value is given} \end{gathered}`

Now, since the necklace after 1 year will be $1.032. From the following equation determine the value of the ring after 1 year:

`\begin{gathered} A=1(1+(0.33)/(100))^(12) \\ A=\text{ \$1.04} \end{gathered}`

Therefore, the ring will value more after 1 year. This is because the ring has a greater annual rate than the necklace.

`\begin{gathered} \text{ Annual rate= 0.33*12} \\ \text{ Annual rate= 3.96\%} \end{gathered}`