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Calculating Future Value of ordinary annuity and annuity due

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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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Solution describes the steps to calculate future value of ordinary annuity and annuity due.

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Solution:

A) Ordinary annuity means that payments are made at the end of periods.
Equal periodic payments=C=$2500
Number of periods=n=10 years
Discount rate=i=8%

Sum of annuity=C/i*((1+i)^n-1)
=2500/8%*((1+8%)^10-1)
=$36216.41
B) Equal periodic payments=C=$500
Number of periods=n=6 years
Discount rate=i=12%

Sum of annuity=C/i*((1+i)^n-1)
=500/12%*((1+12%)^6-1)
=$4057.59
C) Equal periodic payments=C=$30000
Number of periods=n=5 years
Discount rate=i=20%

Sum of ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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