Question

3) Lane and Zack purchased a house for $245,000 in 2016. The house loses 4% of its value each year,

Part A: How much will Lane & Zack's house be worth in 2030?
How will I do this

Answer 1

In 2030 Lane & Zack's house be worth $65,739.27.

Explanation:

Here, as we know The value of property = $245,000

Rate of depreciation = 4% of its present value

Time = From 2016 to 2030 = 14 years

Now, here: Amount depreciated = -( COMPOUND INTEREST on the value)

Step 1: CALCULATE THE COMPOUND INTEREST on P = $245,000

`A = P(1 + (r)/(100) )^t\\\implies A  = (245,000)(1 + (4)/(100) )^(14)  = (245,000)(1 + (4)/(100) )^(14)\\=245,000 ((104)/(100) )^(14)  = 424,260.73`

or, AMOUNT = $424,260.73

Now, AMOUNT = Compound I + Principal

⇒Compound I = A - P = $424,260.73 - $245,000 =$ 179,260

So, the amount of the house by which house depreciates = $ 179,260

⇒The depreciated value = Actual Value - The depreciated amount

= $245,000 - 179,260 = $65,739.27

Hence, in 2030 Lane & Zack's house be worth $65,739.27.