Question

1. Using the values​ below, answer the questions that follow:

Amount of annuity	Interest rate	Deposit period​ (years)
​$500	9​%	10

1. Calculate the future value of the​ annuity, assuming that it is
   1. ​An ordinary annuity. (0.5 marks)
   2. ​An annuity due. (0.5 marks)

2. Compare your findings in parts a​(1) and a​(2). All else being​ identical, which type of annuity—ordinary or annuity due—is preferable as an​ investment? Explain why. (0.5 Marks)

Answer 1

a)

Future value of ordinary annuity is given by the formula

Where C = amount of annuity = $500

i = interest rate = 9%

n = deposit period = 10 years

Future Value of Ordinary Annuity = 500*[(1+9%)¹⁰-1]/9% = 500*(2.367363675-1)/0.09 = 500*1.367363675/0.09

= $7,596.46

Future value of annuity due is given by the formula

Where C = amount of annuity = $500

i = interest rate = 9%

n = deposit period = 10 years

Future Value of Annuity Due = 500*(1+9%)*[(1+9%)¹⁰-1]/9% = 500*(1+0.09)*(2.367363675-1)/0.09

= 500*(1.09)*(1.367363675/0.09) = 500*(1.09)*(15.19292972) = $8,280.15

b)

We can find that the future value of annuity due is higher than that of ordinary annuity

All else being identical, annuity due is preferred as an investment

The future value of annuity due is higher because each payment or deposit happens one period before the corresponding payments in an ordinary annuity. Hence each payment will generate an additional return by a factor of (1+i) compared to an ordinary annuity which will push up the whole future value by a factor of (1+i) for annuity due.