Question

Joey buys a home for $205,900. His home is predicted to increase in value 4% each year. What is the predicted value of his home in 22 years? Round answer to thenearest whole number

Answer 1

Since every year the value of the house increase by 4%, the new value will be the previous value plus 4% of the previous value. To find 4% of a quantity, we just have have to multiply it by 4 and then divide by 100(or, written as a decimal, multiply the number by 0.04).

If we call the previous value of the house as P and the new value as N, the new value after one year will be

`N=P+0.04P=(1+0.04)P=1.04P`

Every year that passes, to get the new value we multiply again by 1.04. The expression for the predicted value after t years is

`N(t)=P_0(1.04)^t`

Where P0 represents the initial value of the house. Evaluating t = 22 on this expression, we have

`N(22)=205,900(1.04)^(22)=487,966.279171\ldots\approx487,966`

The predicted value of his home in 22 years is $487,966.