Question

In 10 ​years, you are planning on retiring and buying a house in​ Oviedo, Florida. The house you are looking at currently costs ​$160,000 and is expected to increase in value each year at a rate of 2 percent. Assuming you can earn 13 percent annually on your​ investments, how much must you invest at the end of each of the next 10 years to be able to buy your dream home when you​ retire?

If the house you are looking at currently costs ​$160,000 and is expected to increase in value each year at a rate of 2 ​percent, what will the value of the house be when you retire in 10 ​years?

Answer 1

Solution

Value of house currently=160000

Increase each year = 2%

Therefore we will use formula of compounding to find the value of house 10 years from now=

Future value= Initial amount*(1+Growth rate)^n

n= Number of years

GroWth rate= 2%

Putting values

Value of house after 10 years=160000*(1+.02)^10

=195039.1072

Now the Future value of annuity amount being saved must be equal to the future value of the house

Future value of annuity= Annuity amount*[((1+r)^n-1)/r]

Future value of annuity= Future value of house=195039.1072

n= number of years

r= Interest rat= 13% in this case

195039.1072= Annuity amount*[((1+.13)^10-1)/.13]

Annuity amount=10588.59

Thus the amount to be deposited each year= 10588.59

If you are satisfied with the answer,please give a thumbs up