Question

A new car depreciates at a rate of 15% per year. What is the expected value of a $25,000 car after 5 years (rounded to nearest whole dollar)? A) $20750 B) $11093 C) $9429 D) $6250

Answer 1

`"B": $11093`

Explanation:

Recall that the formula for compound interest is:

`color(blue)(|bar(ul(color(white)(a/a)A=P(1+r/n)^(n(t))color(white)(a/a)|)))`

where:
`A=`future value
`P=`principal (starting) amount
`r=`annual interest rate, expressed as a decimal
`n=`number of times the interest is compounded in a year
`t=`number of years compound interest occurs for

`1`. Start by substituting your known values into the formula. Note that the annual interest rate is `-0.15` since the car depreciates (becomes lower in value) each year.

`A=25000(1+(-0.15)/1)^(1(5))`

`2`. Solve for `A`.

`A=25000(0.85))^5`

`A=11092.63`

`color(green)(|bar(ul(color(white)(a/a)A~~$11093color(white)(a/a)|)))`