Question

You decide to buy a boat that costs $4200. The normal depreciation for such a boat is 14% per year. If you pay for the boat with a 4-year loan, how much less will the boat be worth after you have paid off the loan?

Answer 1

`$2297.43` to 2 decimal places

Explanation:

`color(blue)("Preamble")`

You did not state if compound or simple interest is to be used.

I choose 'simple interest'

Multiply a number by 1 and you do not change the value.

So for the first year we have:

`"original sum" " - " "sum to be deducted"`

`[$4200xx1]" " -" "[ $4200xx14/100]`

This can be written as:

`$4200(1-14/100)^1" "`for one year
`$4200(1-14/100)^2" "`for two years
`$4200(1-14/100)^3" "`for three years
`$4200(1-14/100)^2" "`for two years
`$4200(1-14/100)^4" "`for years years
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`$4200(1-14/100)^4`

`$4200(86/100)^4" "~~" "$2297.4342....`

`$2297.43` to 2 decimal places

Answer 2

Worth of boat after `4` years is `$2297.43`

Explanation:

Initial cost of boat is `P= $4200`. Depriciation rate;

`d= 14/100=0.14`, Number of years is `n=4`

Worth of boat after `4` years is `W= P(1- d)^4= 4200* (1-0.14)^4` or

`W=4200* (0.86)^4 ~~ $2297.43` [Ans]