 # An Asset You Would Like To Purchase In 5 Years

## Question

Choose an asset you would like to purchase in 5 years. Calculate how much you need to save for the next five years to purchase this asset using the following website: http://www.proteam-corvette.com/1967.html

Base the interest rate on the five year interest rate from the Treasury department.

Calculate the required yearly savings.
Based on the answer from above, what does this say about your feelings of the time value of money?

How much money could be made using the same interest rate with the amount of yearly cash flows which would have been saved for the investment if these amounts had been invested instead?

What are the associated opportunity costs with this type of investment? Explain your answer.

## Solution Preview

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Calculate the required yearly savings.
If the car costs \$180,000 today and we want to save and buy it in five years, we need to make some assumptions about what it will cost in five years.
First, let’s assume that it still costs \$180,000 at that time. That would mean that in today’s terms we need \$180,000/(1+0.0089)^5 = \$172,199.50. This is the present value and now we can use the annuity formula to find out how much we need to save each year by solving for \$172,199.50 = X [PVAF], where PVAF is the present value of an annuity factor = [1/r-1/(r*(1+r)^n] = 4.869223781 because r = 0.0089. Solving for X, we find that the annual savings must be \$35,364.88.
We can check and see that
\$35,364.88(1+0.0089)^4 + \$35,364.88(1+0.0089)^3 + \$35,364.88(1+0.0089)^2 + \$35,364.88(1+0.0089)^1 + \$35,364.88(1+0.0089)^0 = \$180,000.00....

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