Question

Happy Family plans to buy a home in four years. Experts in this area have estimated that the cost of real estate will increase at the rate of 7% per year during that period. This family can make investments that give them a 12% return. If the economic predictions are valid;

a. How much will they have to pay for a house that now costs $ 150,000? 
b. How much will they have to deposit monthly so that after those four years they can buy it? 

Please show process

Answer 1

Happy family palns ti buy aHome after 4 years.

Given Informtaion: Today's House price = 150000, Inflation in real estate = 7%, return on investment =12%

a) How much have to pay for house after 4 years.

You need to calculate the FV of house with using inflation 7%

FV = Pv(1+r)ⁿ

= 150000 (1.07)⁴

= 150000 x 1.31079601

=FV = 196619.40

Price of house in 4 years = $196619.40

b) How much monthy deposit required to buy the house in 4 years. You need to save $1996619.40 in 4 years.

No of periods= 12 x 4 = 48 months,Periodic rate = 12/12= 1% .

[ Assuming Given rate is nominal and deposits due at end of every month starting 1 month from now]

FV = Annuity + Annuity x cumulative annuity factor @ 1% for 47 periods.

[ For cumulative annuity factor refer to your annuity tables or can calculate as it is sum of (1.01) +(1.01)²........+(1.01)⁴⁷ ]

196619.40 = Annuity + Annuity x 37.35369772

196619.40 = Annuity (1 + 60.22260715)

Annuity = 196619.40 / 61.22260715

Annuity = $3211.55 approx

You need to deposit monthly $3211.55 to accumulate the $19661940 to purchase house.