Multiple Select Question

Question

Last month, Maria purchased a new cell phone for $500. The store manager told her that her new cell phone would depreciate by 70% every 6 months. Maria thinks she will want to replace her phone after a while. What will be the value (V) of her phone if she tries to trade it in after 2 years? Select all that apply.
A. v= 500(070)^4

B. v= 500(0.30)^4

C. v = 500(0.30)^2

D. v = 500(1 - 0.70)

E. v = 0.70(500)^4

F. v = 0.30(500)^3

Answer 1

To find the value \( V \) of the phone after 2 years, we need to consider how many 6-month periods there are in 2 years. There are 4 periods of 6 months in 2 years (since 2 years = 24 months and 24 months / 6 months = 4).

Each 6 months, the phone's value retains 30% of its previous value because it depreciates by 70%. Therefore, the value of the phone after each period can be expressed with the formula:

\[ V = 500 \times (0.30)^n \]

where \( n \) is the number of 6-month periods. In this case, after 2 years (or 4 periods), the formula would look like:

\[ V = 500 \times (0.30)^4 \]

Now let's review the provided options:

A. \( V = 500(0.70)^4 \) — Incorrect (should be \( (0.30)^4 \))

B. \( V = 500(0.30)^4 \) — Correct

C. \( V = 500(0.30)^2 \) — Incorrect (correct number of periods is 4)

D. \( V = 500(1 - 0.70) \) — Incorrect (not calculating the value after 4 periods)

E. \( V = 0.70(500)^4 \) — Incorrect (not the right formula for depreciation)

F. \( V = 0.30(500)^3 \) — Incorrect (the formula isn't structured correctly for depreciation)

Based on this analysis, the correct selection is:

B. v = 500(0.30)^4