Question

On June 1 , 2020 Rita Cushing purchases 20 hectares of farm land from her neighbors and agree to pay the purchase in five equal payments of $12000 each due June 1, the first payment to be payable June 1, 2004 , with interest compounded annually at the rate of 15%

what is the purchase price of land?

Answer 1

Assuming that the first payment is made on June 1, 2020,

Here, the payments will be same every year, so it is an annuity. And since the cash flows will start at the beginning of each June 1 so it will be termed as an annuity due. We need to calculate the present value of annuity due. We will use the following formula:

PVAD = P * (1 - (1 / (1 + r)n / r) * (1 + r)

where, PVD is the present value of annuity due, P is the periodical amount = $12000, r is the rate of interest = 15% and n is the time period = 5

Now, putting these values in the above formula, we get,

PVAD = $12000 * (1 - (1 / (1 + 15%)5 / 15%) * (1 + 15%)

PVAD = $12000 * (1 - (1 / (1 + 0.15)5 / 0.15) * (1 + 0.15)

PVAD = $12000 * (1 - (1 / (1.15)5 / 0.15) * (1.15)

PVAD = $12000 * (1 - (1 / 2.0113571875) / 0.15) * (1.15)

PVAD = $12000 * ((1 - 0.49717673529) / 0.15) * (1.15)

PVAD = $12000 * (0.5028232647 / 0.15) * (1.15)

PVAD = $12000 * 3.35215509801 * 1.15

PVAD = $46259.74

So, purchase price of land is $46259.74