Question

a house is losing value at a rate of 5.4% per year. In 2009 the house was worth $131,000.Find the value of the house in 2019

Answer 1

$75,193.91

Explanation:

If V is the original value of the house and it loses value at R% per year

Value at the end of 1st year = V( 1- r) where r = R/100

Value at the end of 2 years = V( 1- r) (1-r) = V(1 - r)²

...
Value at the end of n years = V(1-r)ⁿ

Given
V = 131000

R = 5.4% or r = 5.4/100 = 0.054

n = 10

Value at the end of 10 years (2019-2009) is

131000( 1- 0.054)¹⁰

= 131000(0.946)¹⁰

= 75193.91

So value in 2019 = $75,193.91