Question

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

Answer 1

Answer:

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

Step-by-step 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

$A = P(1 + \frac{r}{100} )^t\\\implies A = (245,000)(1 + \frac{4}{100} )^{14} = (245,000)(1 + \frac{4}{100} )^{14}\\=245,000 (\frac{104}{100} )^{14} = 424,260.73$

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.