
interest
1. With money computed annually at 5%, how long will it take an investment to increase in value from $5,000 to $7,500 ?
2, Assume that you are considering the purchase of land for the location of a new manufacturing facility five years from now. The land can be bought now for $30,000 with taxes at $900 a year and an interest rate of 5%. To justify the purchase price today, the prospective price of the land five years from now should be

1.
$\displaystyle 7500/5000 = 1.5$
$\displaystyle log_{1.05}1.5 = ln1.5 / ln1.05 = 8.31$
So it would be greater than 7500 after 9 years.

That's not a real clear definition of the problem.
1) You don't owe the taxes until you buy it.
2) I guess we're supposed to inflate the Real Estate by the mystery interest rate whose purpose is not stated? $30,000*(1.05^5) = $38,288.45
3) It is not clear at all what to do with the taxes. Do we want to include prepmayment of taxes as part of the purchase price? Are taxes paid annually, in advance? $900*(1 + v + v^2 + ...) = $900/(i*v) = $900/d = $18,900
4) Is there an Internal Rate of Return on this investment, or are we just eating it because we need the real estate?
Just guessing. You may have discussed some specifics in class, but it appears you did not share them with us.