This present value of annuity calculator estimates the value in today’s money of a series of future payments of the same amount for a number of periods the interest is compounded (due or ordinary annuity). There is more information on how to determine this financial indicator below the form.
How does this present value of annuity calculator work?
This financial application can help you determine the present value of a series of fixed annuity payments, either ordinary (made at the end of each period) or due (at the beginning of each one) by taking into account these figures:
 Regular payment which is should be the same amount you expect to receive/pay each time period.
 Interest rate per period which is a constant (most often referred to as annual) rate for the cost for the money use.
 Number of time periods which refers to the time frame in which the interest is compounded (year, twice a year, month.) and should refer to the same time period as the interest rate per period. For instance if the interest is annually, then the Number of periods by default will be expressed in years.
The algorithm behind this present value of annuity calculator is based on the formulas explained as follows:

Present Value of Annuity is calculated depending on the annuity type
 In ordinary case the equation is:
[PVOA] = RP/r * (1  (1/(1 + r)^NP))
 In due case the formula is:
[PVAD] = PVOA * (1 + r)

Interest [B] = [FV] – [VP]

Regular payments total value [VP] = RP * NP

Future Value [FV] = Present value * [(1 + r)^NP]

Compound interest factor [C] = 1 + ([B]/[VP])
Where:
RP = Regular payment
FV = Future value
NP = Number of time periods
r = Interest rate per period
Apart from the figures presented above this calculator also generates a report showing the exact evolution of the annuities present value per each period.
Example of two results
Case 1: Let’s assume an ordinary annuity with a regular payment per year is $10,000, over 25 years with 3.5% annual interest rate. This will result in:
■ Present Value of Ordinary Annuity: $164,815.15
■ Interest: $139,498.57
■ Regular payments total value: $250,000.00
■ Future Value: $389,498.57
■ Compound interest factor: 1.55799
The evolution of the present value of annuity per each period is presented below:
Period  Starting balance  Payment  Interest  Ending Balance 

1  $0.00  $10,000.00  $0.00  $10,000.00 
2  $10,000.00  $10,000.00  $350.00  $20,350.00 
3  $20,350.00  $10,000.00  $712.25  $31,062.25 
4  $31,062.25  $10,000.00  $1,087.18  $42,149.43 
5  $42,149.43  $10,000.00  $1,475.23  $53,624.66 
6  $53,624.66  $10,000.00  $1,876.86  $65,501.52 
7  $65,501.52  $10,000.00  $2,292.55  $77,794.08 
8  $77,794.08  $10,000.00  $2,722.79  $90,516.87 
9  $90,516.87  $10,000.00  $3,168.09  $103,684.96 
10  $103,684.96  $10,000.00  $3,628.97  $117,313.93 
11  $117,313.93  $10,000.00  $4,105.99  $131,419.92 
12  $131,419.92  $10,000.00  $4,599.70  $146,019.62 
13  $146,019.62  $10,000.00  $5,110.69  $161,130.30 
14  $161,130.30  $10,000.00  $5,639.56  $176,769.86 
15  $176,769.86  $10,000.00  $6,186.95  $192,956.81 
16  $192,956.81  $10,000.00  $6,753.49  $209,710.30 
17  $209,710.30  $10,000.00  $7,339.86  $227,050.16 
18  $227,050.16  $10,000.00  $7,946.76  $244,996.91 
19  $244,996.91  $10,000.00  $8,574.89  $263,571.80 
20  $263,571.80  $10,000.00  $9,225.01  $282,796.82 
21  $282,796.82  $10,000.00  $9,897.89  $302,694.71 
22  $302,694.71  $10,000.00  $10,594.31  $323,289.02 
23  $323,289.02  $10,000.00  $11,315.12  $344,604.14 
24  $344,604.14  $10,000.00  $12,061.14  $366,665.28 
25  $366,665.28  $10,000.00  $12,833.28  $389,498.57 
Case 2: Let’s take the example of a due annuity with the same characteristics and see the difference in figures:
■ Present Value of Due Annuity: $170,583.68
■ Interest: $153,131.02
■ Regular payments total value: $250,000.00
■ Future Value: $403,131.02
■ Compound interest factor: 1.61252
The evolution of the present value of annuity per each period is presented below:
Period  Starting balance  Payment  Interest  Ending Balance 

1  $0.00  $10,000.00  $350.00  $10,350.00 
2  $10,350.00  $10,000.00  $712.25  $21,062.25 
3  $21,062.25  $10,000.00  $1,087.18  $32,149.43 
4  $32,149.43  $10,000.00  $1,475.23  $43,624.66 
5  $43,624.66  $10,000.00  $1,876.86  $55,501.52 
6  $55,501.52  $10,000.00  $2,292.55  $67,794.08 
7  $67,794.08  $10,000.00  $2,722.79  $80,516.87 
8  $80,516.87  $10,000.00  $3,168.09  $93,684.96 
9  $93,684.96  $10,000.00  $3,628.97  $107,313.93 
10  $107,313.93  $10,000.00  $4,105.99  $121,419.92 
11  $121,419.92  $10,000.00  $4,599.70  $136,019.62 
12  $136,019.62  $10,000.00  $5,110.69  $151,130.30 
13  $151,130.30  $10,000.00  $5,639.56  $166,769.86 
14  $166,769.86  $10,000.00  $6,186.95  $182,956.81 
15  $182,956.81  $10,000.00  $6,753.49  $199,710.30 
16  $199,710.30  $10,000.00  $7,339.86  $217,050.16 
17  $217,050.16  $10,000.00  $7,946.76  $234,996.91 
18  $234,996.91  $10,000.00  $8,574.89  $253,571.80 
19  $253,571.80  $10,000.00  $9,225.01  $272,796.82 
20  $272,796.82  $10,000.00  $9,897.89  $292,694.71 
21  $292,694.71  $10,000.00  $10,594.31  $313,289.02 
22  $313,289.02  $10,000.00  $11,315.12  $334,604.14 
23  $334,604.14  $10,000.00  $12,061.14  $356,665.28 
24  $356,665.28  $10,000.00  $12,833.28  $379,498.57 
25  $379,498.57  $10,000.00  $13,632.45  $403,131.02 
What are annuities?
In finance theory, these are a series of fixed payments either you pay or that are paid to you with a specific frequency as negotiated between the parties, made over a certain period of time. For instance payments most often can be annually, semiannually, quarterly or monthly. By taking account of the moment the annuity is paid there are two types:

Ordinary annuity which assumes that the payments are made at the end of each period.

Annuity due which means they are paid at the beginning of each period.
By comparison between the two, the total interest paid figure is greater in an annuity due than in case of an ordinary one.
06 Feb, 2015  0 comments
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