Question

You plan to retire in 15 years and buy a house in​ Oviedo, Florida. The house you are looking at currently costs $150,000 and is expected to increase in value each year at a rate of 6 percent. Assuming you can earn 9 percent annually on your​ investments, how much must you invest at the end of each of the next 15 years to be able to buy your dream home when you​ retire?

a.  If the house you are looking at currently costs $150,000 and is expected to increase in value each year at a rate of 6 ​percent, what will the value of the house be when you retire in 15 ​years? ​(Round to the nearest​ cent.)

b.  Assuming you can earn 9 percent annually on your​ investments, how much must you invest at the end of each of the next 15 years to be able to buy your dream home when you​ retire?

Answer 1

a)

Value of house in 15 years can be computed using formula for FV of single sum as:

FV = PV x (1+r) n

PV = Present value of house = $ 150,000

r = Rate of interest = 0.06

n = Number of periods = 15

FV = $ 150,000 x (1+0.06)15

      = $ 150,000 x (1.06)15

      = $ 150,000 x 2.39655819309969

      = $ 359,483.728964954 or $ 359,483.73

Value of the house will be $ 359,483.73 in 15 years.

b)

Formula for future value of annuity can be used to compute annual cash deposit as:

FV = P x [(1+r) n -1]/r

P = FV/[(1+r) n -1]/r

FV = Future value of deposits = $ 359,483.73

P = Periodic cash deposit

r = Rate of return = 0.09

n = Number of periods = 15

P = $ 359,483.73 / [(1+0.09) 15 -1]/0.09

    = $ 359,483.73 / [(1.09) 15 -1]/0.09

    = $ 359,483.73 / [(3.64248245968752-1)/0.09]

   = $ 359,483.73 / [(2.64248245968752/0.09)

    = $ 359,483.73 / 29.3609162187503

    = $ 12,243.6141747657 or $ 12,243.61

We need to save $ 12,243.61 annually to purchase the house in 15 years.