Question

​(Future value of an annuity​) In 9 years you are planning on retiring and buying a house in​ Oviedo, Florida. The house you are looking at currently costs ​$130,000 and is expected to increase in value each year at a rate of 6 percent. Assuming you can earn 15 percent annually on your​ investments, how much must you invest at the end of each of the next 9 years to be able to buy your dream home when you​ retire?

a. If the house you are looking at currently costs ​$130,000 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 9 ​years? ​$______ ​(Round to the nearest​ cent.)

b. Assuming you can earn 15 percent annually on your​ investments, how much must you invest at the end of each of the next 9

years to be able to buy your dream home when you​ retire? ​$_______ ​(Round to the nearest​ cent.)

Answer 1

a) Given present value of house = 130000

Future value of house at 6% increment for 9 years is given as = Present value*(1+ Increment rate)^time

=130000*(1+ 6%)^9

=130000*1.68948

=219632.40

Hence the future value of House = 219632.40

b) Let the annual payment = X

Future value of annual payment = X*(1+ Investment return income)^8+X*(1+ Investment return income)^7+X*(1+ Investment return income)^6+X*(1+ Investment return income)^5+X*(1+ Investment return income)^4+X*(1+ Investment return income)^3+X*(1+ Investment return income)^2+X*(1+ Investment return income)^1+X*(1+ Investment return income)^0

=X*(1.15)^8+X*(1.15)^7+X*(1.15)^6+X*(1.15)^5+X*(1.15)^4+X*(1.15)^3+X*(1.15)^2+X*(1.15)^1+X*(1.15)^0

=3.059X+2.66X+2.313X+2.011X+1.749X+1.521X+1.323X+1.15X+X

=16.786X

Calculated above =future value of House = 219632.40

Hence 16.786X=219632.40

X=219632.40/16.786

=13084.26

Hence annual payment of 13084.26 shall be made for 9 years earning 15% return will be equal to future value of house