Blackstone Company purchased a new software system costing $35,000. To finance the purchase, Blackstone signed a contract agreeing to pay the cost over the next 8 years, with a payment due every six months; the first payment will be made six months from the date of purchase. Blackstone's usual interest rate is 10%. What is the amount of the payment required (rounded to the nearest dollar) ? Select one: a. 16,030 b. 6,560 c. 3,229 d. 2,575 e. None of the above

c. 3,229

Explanation:

It is a present value because the company purchased a new software today. Again, the payment is distributed by yearly or monthly payment up to 8 years, so, it is an ordinary annuity of present value. Since the payment is due every six months, it is a semiannual payment.

To determine the payment, we have to calculate the ordinary annuity of present value:

PVoa = PMT x [{1 - (1+i/m) ^ (-n*m) } / (i/m) ], as it is a semiannual payment.

Given,

PVoa = $35,000

interest rate, i = 10% = 0.10

Number of payments per year, m = 2

therefore, i/m = 0.10/2 = 0.05

Number of year, n = 8

Putting those values in the PVoa formula, we can get,

$35,000 = PMT x [{1 - (1+0.05) ^ (-8*2) }/0.05]

or, $35,000 = PMT x [ (1 - 0.4581) / 0.05]

or, $35,000 = PMT x 10.83777

or, PMT = $35,000/10.83777

or, PMT = $3,229

It means Blackstone Company has to pay $3,229 as his first payment after the six months.