(Future value of an annuity) In 6 years you are planning on retiring and buying
ID: 1174673 • Letter: #
Question
(Future value of an annuity) In 6 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 5 percent. Assuming you can earn 9 percent annually on your investments, how much must you invest at the end of each of the next 6 years to be able to buy your dream home when you retire? a. If the house you are looking at currently costs $160,000 and is expected to increase in value each year at a rate of 5 percent, what will the value of the house be when you retire in 6 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 6 years to be able to buy your dream home when you retire? Round to the nearest cent.)Explanation / Answer
a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence
A=$160,000*(1.05)^6
=$160,000*1.340095641
=$214415.30(Approx).
2.
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
214415.30=Annuity[(1.09)^6-1]/0.09
214415.30=Annuity*7.523334565
Annuity=214415.30/7.523334565
which is equal to
=$28500.04(Approx).
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