Future Value Annuity (FVA) Homework Help & Future Value Annuity (FVA) Tutoring
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Future Value – Annuity
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.
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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