Question

Marianne buys a house for 150,000 and the value of the house increases at a rate of 1.2% per year.How much will the house be worth in 10 years .Round to the nearest dollar.

Answer 1

To determine the value of the house in x number of years, we need to derive an equation that would relate the value of the house, the rate of increase and the number of years. If we calculate manually, we would do as follows:

V(1) = 150000 + 150000(0.012)
V(2) = 150000 + (150000 + 150000(0.012))(0.012)
V(3) = .............

We need to do this up to 10 years. It would be a long and tedious process. We need to simplify the expression as follows:

We factor out the initial amount of the house and simplify further what is inside the parentheses. This would give us
V(x) = 150000 (1 + 0.012)^x

Substitute 10 to x,
V(x) = 150000 (1 + 0.012)^x10
V(10) = 169003.77