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Future Value Annuity

Assignment / Homework Help
An annuity is a stream of equal annual cash flows occurring at regular intervals of time. When the cash flows occur at the end of each period, the annuity is called as an ordinary annuity or a deferred annuity. When the cash flows occur at the beginning of each period, the annuity is called as an annuity due. The Future Value of an Annuity is given by the following formula:
FV An = A (1 + r)n-1 + A (1 + r)n-2 + ........ A
= A [(1 + r)n -1] / r
Where
FV An = Future value of an annuity at time n
A = Annuity periodic amount
r = Interest rate
n = Number of periods

Example: A person deposits $10,000 annually in a bank for 5 years which earns an interest of 9%, compounded annually. Let us calculate the future value of his series of deposits at the end of 5 years.

FV An = A [(1 + r)n - 1] / r
A = $10,000
r = 9% or .09
n = 5

Future value of annuity = $10,000 [(1 + 0.09)5 - 1] / 0.09
= $59,847.11

Time Line for an Annuity

1 2 3 4 5
$ 10,000 $ 10,000 $ 10,000 $ 10,000 $ 10,000
+









$ 10,900 +









$ 11,881 +









$ 12,950.29 +









  $ 14,115.82



TOTAL   $ 59,847.11


Example:

To find out the required annual deposits to accumulate a sum in future:

A company needs to accumulate $100 million in the next 6 years to retire its long-term debts. Calculate the amount the company needs to deposit annually in a fund which earns 14% interest per annum.

FV An = A [(1 + r)n - 1] / r
r = .14 or 14%
n = 6
FV An = $100 million

Substituting the values:
$100 million = A [(1 + 0.14)6 - 1] / 0.14
A = $100 million / 8.5355187 = $11.716 million


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