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Annuity

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Katrina Washington is currently employed as a computer programmer by Megatel Company. Her dream is to start her own computer software firm. to provide cash to state her own business in six yers she will invest $10,000 today. She thinks the investment will earn a 12% annual return.

a. How much would Katrina have in her account at the end of six yrs if she earns 12% onthe investment? How much of this would be interest earned during the six years?

b. Assume, instead Katrina has decided to she needs $20,000 to begin business. She wants toinvest equal amounts at the end of each year for the next six years to accumulate the $20,000 needed at that time.

i. How much must bhe invested each year, assuming that it earns 12% interest?
ii. How much will the investment be worth at the end of each of the next six years?
iii. How much will Katrina have put into the account over the six years?
iv. How much interest will be earned over the six years?

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Solution Preview

Formula for calculation of future value of annuity =

Future Value of Annuity,F.V = R [ (1+i)^n -1]/i
Where,F.V.= the future value of an annuity.
R = the periodic payment in an annuity (the amortized payment)=$10000
i = Interest rate per period=12% per annum
n= number of periods=6 years

F.V = R [ (1+i)^n -1]/i= 10000 [ (1+12/100)^6 -1]/(12/100)=81151.89
Thus, Katrina will have ...

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Calculating Future Value of ordinary annuity and annuity due

Future Value of annuity : For each case in the accompanying table, answer the question that follow.
Amount of Interest Deposit period
Case annuity rate (years)
A $ 2,500 8% 10
B 500 12 6
C 30,000 20 5
D 11,500 9 8
E 6,000 14 30

a. Calculate the future value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b. Compare your finding in parts a (1) and a (2). All else being identical, which type of annuity - ordinary or annuity due - is preferable? Explain why?

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