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You wish to buy a cabin in 15 years. TODAY, the cabin costs $150,000. You believe the price of the cabin will inflate at 4% annually. You want to invest a single amount of money (lump sum) today and have the money grow to equal the future purchase price of the cabin 15 years from now. If you can earn 10% annually on your investments, how much do you need to invest NOW, in order to be able to purchase the cabin?

Respuesta :

TomShelby

Answer:

I will need to invest 64,669.73 dollars now.

Explanation:

We will calcualte the future value of the cabin considering the inflation:

[tex]Principal \: (1+ inflation )^{time} = Amount[/tex]

Principal 150,000.00

time  15 years

inflation 0.04000

[tex]150000 \: (1+ 0.04)^{15} = Amount[/tex]

Amount 270,141.53

Then we calculate the present value of the lump sum at 15 years discounted at 10% which is the yield of the funds

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  270,141.53

time   15 years

rate  0.10

[tex]\frac{270141.53}{(1 + 0.1)^{15} } = PV[/tex]  

PV   64,669.73

we would need to deposit 64,669.73 today to get enough cash to purchase the bcabin in 15 years.