Question

Marie and Alex just paid $250,000 for a house. They made a down payment of $50,000 and assumed a 30-year $200,000 mortgage with a fixed annual interest rate of 5.50%. The house will serve as a residence for several years, but Marie and Alex also view it as an investment, as property values in the neighborhood are projected to increase at a rate of 5% per year in the near future. Property taxes on their home will be $4,236 the first year and are expected to increase 3% a year. Homeowners insurance will cost $632 the first year and is expected to increase at a rate of 2% each year. The couple plans to sell the house after eight years. Answer the following questions.

What will the couple pay in property taxes over the 8 years?

What will the couple pay in homeowners insurance over the 8 years?

Answer 1

Both the expenses are in the form of a geometric series, whose
sum is given by:
A*[(1-r)^n/(1-r)]
Sum of property taxes for 8 years = 4236*((1-1.03^8)/(1-1.03)) =	$         37,668
Sum of property taxes for 8 years = 632*((1-1.02^8)/(1-1.02)) =	$           5,424