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

1)

Account value accumulated in 4 years = Invested Amount * (1 + interest rate)^{no of periods}

Account value accumulated in 4 years = $5100 * (1 + 11%)⁴

Account value accumulated in 4 years = $7742.16

Account value accumulated in 8 years = Invested Amount * (1 + interest rate)^{no of periods}

Account value accumulated in 8 years = $5100 * (1 + 11%)⁸

Account value accumulated in 8 years = $11,753.14

Account value accumulated in 12 years = Invested Amount * (1 + interest rate)^{no of periods}

Account value accumulated in 12 years = $5100 * (1 + 11%)¹²

Account value accumulated in 12 years = $17,842.10

2)

Value of ordinary annuity = Annuity / (1 + interest rate)^period+ ,,,,,+ Annuity / (1 + interest rate)^period​​​​​​​

Value of ordinary annuity = Annuity * (1 - (1 + interest rate)^{-no of periods}) / interest rate

Value of ordinary annuity = $500 * (1 - (1 + 9%)^-10) / 9%

Value of ordinary annuity = $3208.83

Value of annuity due = Annuity + Annuity / (1 + interest rate)^period+ ,,,,,+ Annuity / (1 + interest rate)^period​​​​​​​

Value of annuity due = Annuity + Annuity * (1 - (1 + interest rate)^{-no of periods}) / interest rate

Value of annuity due = $500 + $500 * (1 - (1 + 9%)^-9) / 9%

Value of annuity due = $3497.62

Annuity due is a better investment since the value of the money received today is more than the value received in the future. Annuity due makes payments at the beginning of the year while the ordinary annuity makes payments at the end of each year. The discounting periods for Annuity due are lower than ordinary annuity.