Question

 

FIN101

1. You have $5,100 to invest today at 11​% interest compounded annually. Find how much you will have accumulated in the account at the end of​: (0.5 Marks each)

(1) 4 years,

(2) 8 years, and​

(3) 12 years.

2. 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

Calculation of Future Value

FV = PV (1+r)ⁿ

FV = Future Value

PV = Present Value

r = Interest or discount rate

n = Number of periods or years

(1) FV = $5,100(1+ 0.11)⁴

FV = $5,100(1.11)⁴

FV = $7,742.16

(2) FV = $5,100(1+ 0.11)⁸

FV = $5,100(1.11)⁸

FV = $11,753.14

(3) FV = $5,100(1+ 0.11)¹²

FV = $5,100(1.11)¹²

FV = $17,842.10

Calculation of Future Value of Annuity

Future Value of an Ordinary Annuity

FV_{Ordinary Annuity}  = P X ([1 + I]^N - 1 ) / I

P= Payment Amount

I = Interest (discount) rate

N = Number of payments

FV = $500 X ([1 + 0.09]^10 - 1) / 0.09

FV = $500 X ([1.09]^10 - 1) / 0.09

FV = $7,596.46

Future Value of an Annuity Due

FV_{Annuity Due} = P X ([1 + I]^N - 1 ) / I X (1 + I)

FV = $500 X ([1 + 0.09]^10 - 1) / 0.09 X (1 + 0.09)

FV = $8,280.15

An Ordinary Annuity is an annuity where cash flows occur at the end of the interest period. An Annuity Due is an annuity where cash flows occur at the beginning of the interest period. As a result, there is one less discounting period for an annuity due, and therefore its present value is higher than an ordinary annuity.

If you're liable for making payments on an annuity, you'll benefit from having an ordinary annuity because it allows you to hold onto your money for a longer amount of time. However, if you're on the receiving end of annuity payments, you'll benefit from having an annuity due, as you'll receive your payment sooner.