Potash Corporation financed the purchase of a building by making semiannual payments of $20,000 a year for the next twenty years,with the first payment due one year from today.The purchase cost of the building is considered to be the present value of those payments.What was the purchase cost of the building to Potash assuming an annual interest rate of 10%?
A)$363,636
B)$343,182
C)$192,883
D)$170,271

Question

Quizplus · Accepted Answer

This question requires calculating the present value of an annuity. We can use the formula:

PV = A * [1 - (1+r)^(-n)] / r

Where:
PV = present value 
A = the annual payment 
r = the interest rate per period (semiannual in this case). Since the annual interest rate is 10%, the semiannual rate is 5%. 
n = the number of periods (in this case, 20 years * 2 semiannual payments per year = 40 periods)

Plugging in the values: 
PV = 20,000 * [1 - (1+0.05)^(-40)] / 0.05 
PV = $343,182

Therefore, the purchase cost of the building to Potash is $343,182 (option B).

Potash Corporation Financed the Purchase of a Building by Making