Question

You are set to receive an annual payment of 10600 per year for the next 12 years. Assume the interest rate is 5.5 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year

Answer 1

Formula for present value of ordinary annuity is:

PV = P x [1-(1+r)^-n/r]      

P = Periodic Payment = $ 10,600

r = Rate per period = 5.5 % or 0.055 p.a.

n = Numbers of periods = 12

PV = $ 10,600 x [1-(1+0.055)^-12/0.055]

     = $ 10,600 x [1-(1.055)^-12/0.055]

      = $ 10,600 x [(1-0.52598152)/0.055]

      = $ 10,600 x (0.47401848/0.055)

      = $ 10,600 x 8.61851785 = $ 91,356.29

Formula for present value of annuity due is:

PV = P + P x [1-(1+r)^-(n-1)/r]

      = $ 10,600 + $ 10,600 x [1-(1+0.055)^-(12-1)/0.055]            

      = $ 10,600 + $ 10,600 x [1-(1.055)^-11/0.055]

      = $ 10,600 + $ 10,600 x [(1-0.554911)/0.055]

      = $ 10,600 + $ 10,600 x (0.445089/0.055)

      = $ 10,600 + $ 10,600 x 8.092536

     = $ 10,600 + $ 85,780.89 = $ 96,380.89

Payment difference between PV of annuity due and ordinary annuity

                                     = $ 96,380.89 - $ 91,356.29 = $ 5,024.60

$ 5,024.60 is extra paid if payment is received at the beginning of the month rather than ending.