Question

Connie Buecher’s grandmother will cut a check worth $25,220.00 every four months for 14 years. How much is this cash flow worth to them today if the payments begin today? Assume a discount rate of 5.00%.

a. $502,515.46

b. $1,541,755.57

c. $770,042.99

d. $253,804.45

Answer 1

Amount to be received 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 41 periods at the end of each period starting from 1 period from now, and we will also add an additional annuity that will be received today. Effectively, we have a total of PV of next 41 installments and today’s installment.

Where, P = Annuity = 25220, i = Interest Rate = 0.05/3 = 0.016666, n = Number of Periods = 42-1 = 41

Therefore, Present Value = PV of next 4 Installments + Today’s Installment = [25220*{1-((1+0.016666)^-41)}/0.016666]+25220 = 744822.99+25220 = $770042.99