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Calculate the present value to purchase a lot of land if $18,000 is put down and $2,000 is paid per quarter...

26. Calculate the present value to purchase a lot of land if $18,000 is put down and $2,000 is paid per quarter for 5 years. Assume that there is 6% interest that is compounded quarterly.
If the cash price for the land is $25,000, is it better to pay cash or finance the purchase?
According to the Present Value of an Annuity Table, at 1.5% interest for 5 years, the factor is 17.16864.
○ $22,782.64; it is better to finance the purchase
○ $4,782.64; it is better to finance the purchase
○ $52,337.28; it is better to pay $25,000 cash
○ $27,565.28; it is better to pay $25,000 cash

Answer

To calculate the present value of the annuity, use the formula:

PV = PMT × PVIFA

Where:

  • PV = Present Value
  • PMT = Payment per period ($2,000)
  • PVIFA = Present Value Interest Factor of Annuity (17.16864)

Substitute the values:

PV = $2,000 × 17.16864 = $34,337.28

Adding the down payment:

Total Present Value = $34,337.28 + $18,000 = $52,337.28

Since $52,337.28 is greater than the cash price of $25,000, it is better to pay $25,000 cash.

  1. $52,337.28; it is better to pay $25,000 cash

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