David bought a car for $15,000. It depreciates 14% a year. How much will it be worth in 5 years?

Question

Isaiah Anthony · Accepted Answer

After 5 years, its worth will be #$7056#

Table 1 displays the car's value.

At the end of year Value (US dollars) 1 #$12,900# 2 #$11,094# 3 #$9,541# 4 #$8,205# 5 #$7,056#

At the end of the 5th year, his car worths #$7,056#

Please take note that in this computation, I did not include cents.

Eva Adamson · Answer

#=$7,056.41#

If the car depreciates by #14%# per year, it will be worth #86%# of the value after a year. #100%-14% = 86%#

This happens for #5# years in a row, which would mean:

#15,000 xx0.86 xx0.86 ........ 5# times

Apply the compound growth-depreciation formula.

Value #= P(1-0.14)^5#

#= 15,000(0.86)^5#

#=$7,056.41#

Genesis Allen · Answer

undefined To find the value of the car after 5 years, you can use the formula for exponential decay:

$$ \text{Value after } n \text{ years} = \text{Initial value} \times (1 - \text{Rate of depreciation})^n $$

Given:
- Initial value ($P$) = $15,000
- Rate of depreciation ($r$) = 14% or 0.14
- Number of years ($n$) = 5

Plug these values into the formula:

$$ \text{Value after 5 years} = 15,000 \times (1 - 0.14)^5 $$

Calculate:
$$ \text{Value after 5 years} = 15,000 \times (0.86)^5 $$

$$ \text{Value after 5 years} \approx 15000 \times 0.374 $$

$$ \text{Value after 5 years} \approx \$5,610 $$

So, the car will be worth approximately $5,610 after 5 years.