### Annuity

The annuity is a financial term; mostly addressed in the financial theory to explain the lapsing flow of fixed payments that are considered over the set period of time. The interest rates and future value that are the concepts ruled by time value of money are mostly associated to annuity while considering payment streams. The insurance monthly payments, home mortgage payments and regular deposits to saving accounts are the general or routine examples of annuity that is often observed from day to day. The dates regarding payments decide the annuity type.

### Future Value of Annuity

The successive payment or receipts that are received on the regular basis or equally spaced intervals is termed as annuity. In ordinary annuity the receipt session is held at the end while in annuity due the payments are to be submitted at the beginning of the session or the period.

The future value of annuity calculates the future value generated by the calculating the total equal payments in the stream at the given rate at the predefined time span.

### Formula of Future Annuity Calculation

**FV = PMT [((1 + i)^{n} – 1) / i]**

The FV as evident from the name is future value of annuity, PMT refers to Periodic payment amount, where as n and i refers to number of compounding periods and interest rate respectively.

The future annuity actually explains the worth of certain collected payment after the streamlined payment schedule in the future, when all payments are made. The future annuity actually measures the additional interest not only for the amount paid but also to those values of capital that is borrowed from the bank or leasing agency, so assets and liabilities both are included in this context. The payment amount that is PMT can be can also be calculated from the above equation by making certain rearrangements in the above equation to reach the desired future value either by the depositor or the buyer.

### Example of FV of Annuity

The future value of annuity works exceptionally well while computing the values for ordinary future annuity in which the composite fraction is to be calculated at the end of payment sessions. For instance if some one is investing or borrowing $30 each year for four years and wants to be illustrated for the compounded value each year at the interest of 10% for the specified set of years, then future value of annuity would be employed through the described formula.

The values would be input in the formula as PMT = 30.00, i = 0.1, n= 4, the computation would be as follows;

**FV = PMT [((1 + i)^{n} – 1) / i]** = 30.00((1+0.1)

^{3}– 1/0.1) = $99.33

The accumulated value for $30 after three years at 10% interest would be $99.33 for the depositor or borrower, what ever the case may be. The above calculations evidently clears that future value for payment sum of $90 is bigger than that by $9.33. The interest for all the payments is made at the time of deposition except the last one. For the first years for instance the power of three would be converted to two and profit of two years would be earned that would be $36.3. The last year profit would be just for one installment that would be $ 33. in this way each year’s profit or interest can be calculated systematically.

### References

• Finite Mathematics, Eighth Edition, by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. Published by Addison Wesley. ISBN 032122826X

• Lasher, William (2008). Practical financial management. Mason, Ohio: Thomson South-Western. p. 230. ISBN 0-324-42262-8.