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Suppose your parents have 2 options to purchase a plot of land on which they plan to build a barn. Option...

16. Suppose your parents have 2 options to purchase a plot of land on which they plan to build a barn.
Option 1: They can purchase the land for $30,000 cash.
Option 2: They can purchase the land with $7,500 down, and then pay $2,500 semi-annually for the next 10 years, at an interest rate of 5%.
Calculate the present value for both options, and tell which will save them the most money.
(According to the Present Value of an Annuity Table, at 2.5% interest for 10 years, the factor is 8.75206.)
Option 1 will save your parents the most money.
Option 2 will save your parents the most money.
The options both cost the same, so neither one will save them money.
It is not possible to determine which option will save the most money because the question does not state how large the barn will be.

Answer

Option 1: The cost is $30,000 cash.

Option 2: Calculate the present value of the payments:

  1. Down payment: $7,500
  2. Semi-annual payments: $2,500 for 10 years (20 payments total)
  3. Present Value of Annuity: $2,500 * 8.75206 = $21,880.15
  4. Total Present Value for Option 2: $7,500 + $21,880.15 = $29,380.15

Therefore, Option 2 will save your parents the most money as it has a lower present value cost of $29,380.15 compared to $30,000 for Option 1.

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