You have $5,100 to invest toda
FIN101
- 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.
- Using the values below, answer the questions that follow:
|
Amount of annuity |
Interest rate |
Deposit period (years) |
|
|
$500 |
9% |
10 |
- Calculate the future value of the annuity, assuming that it is
- An ordinary annuity. (0.5 marks)
- An annuity due. (0.5 marks)
- 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)
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 + interestrate)period+ ,,,,,+ Annuity / (1 + interestrate)period
Value of ordinary annuity = Annuity * (1 – (1 + interestrate)-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 + interestrate)period+ ,,,,,+ Annuity / (1 + interestrate)period
Value of annuity due = Annuity + Annuity * (1 – (1 + interestrate)-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 moneyreceived today is more than the value received in the future.Annuity due makes payments at the beginning of the year while theordinary annuity makes payments at the end of each year. Thediscounting periods for Annuity due are lower than ordinaryannuity.
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