Question

What is the present value of the following annuity?
$3,868 every half year at the beginning of the period for the next 3 years, discounted back to the present at 6.78 percent per year, compounded semiannually. Round the answer to two decimal places.

Answer 1

Amount to be invest at the BEGINNING of each year = PV of Annuity = P*[1-{(1+i)^-n}]/i

Note: For the purpose of calculation (so that formula can be applied), it will be considered that amount will be received for 5 periods at the end of each half year starting from half1 year from now, and we will also add an additional annuity that will be received today. Effectively, we have a total of PV of next 5 installments and today’s installment.

Where, P = Annuity = 3868, i = Interest Rate = 0.0678/2 = 0.0339, n = Number of Periods = 6-1 = 5

Therefore, Present Value = PV of next 5 Installments + Today’s Installment = [3868*{1-((1+0.0339)^-5)}/0.0339]+3868 = 17518.76+3868 = $21386.76