This future value of annuity calculator estimates the value (FV) of a series of fixed future annuity payments at a specific interest rate and for a no. of periods the interest is compounded (either ordinary or due annuity). There is more info on this topic below the form.

Annuity payment:*
\$
Interest rate per period:*
%
Number of time periods:*
Annuity type:*

## How does this future value of annuity calculator work?

This form can help you estimate the FV of a series of fixed annuity payments by considering these variables:

• Annuity payment which is constant per each 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 that represents the time frame in which the regular annuity payment is made and the interest is compounded (year, twice a year, month.). Please remember that each period is the same as the one for the interest rate. For example if the interest rate is compounded monthly, then the No. of periods by default will be given in months.

The algorithm behind this future value of annuity calculator applies the equations detailed here:

• Present Value of Annuity (PV..) is estimated by taking account of the annuity type

- If ordinary then the formula is:

[PVOA] = AP/r * (1 - (1/(1 + r)^N))

- If due then the formula is:

[PVAD] = PVOA * (1 + r)

• Interest [B] = [FV] – [VP]
• Annuity payments total value [VP] = AP * N
• Future Value [FV] = PV... * [(1 + r)^N]
• Compound interest factor [C] = 1 + ([B]/[VP])

Where:

AP = Annuity payment

FV = Future value

N = No. of time periods

r = Interest rate per period

Together with the figures explained in the above, this calculator displays a details report showing the growth per each period.

## Example of two calculations

Case 1: Let’s consider an ordinary annuity with a payment per month of \$1,000, over 5 years (which translates into 5 * 12 = 60 time periods) with 0.5% monthly compound interest rate. This will result in:

Future Value of Ordinary Annuity: \$69,770.03

Present Value: \$51,725.56

Interest: \$9,770.03

Annuity payments total value: \$60,000.00

Compound interest factor: 1.16283

The evolution per each period is presented below:

PeriodStarting balancePaymentInterestEnding Balance
1 \$0.00 \$1,000.00 \$0.00 \$1,000.00
2 \$1,000.00 \$1,000.00 \$5.00 \$2,005.00
3 \$2,005.00 \$1,000.00 \$10.02 \$3,015.02
4 \$3,015.02 \$1,000.00 \$15.08 \$4,030.10
5 \$4,030.10 \$1,000.00 \$20.15 \$5,050.25
6 \$5,050.25 \$1,000.00 \$25.25 \$6,075.50
7 \$6,075.50 \$1,000.00 \$30.38 \$7,105.88
8 \$7,105.88 \$1,000.00 \$35.53 \$8,141.41
9 \$8,141.41 \$1,000.00 \$40.71 \$9,182.12
10 \$9,182.12 \$1,000.00 \$45.91 \$10,228.03
11 \$10,228.03 \$1,000.00 \$51.14 \$11,279.17
12 \$11,279.17 \$1,000.00 \$56.40 \$12,335.56
13 \$12,335.56 \$1,000.00 \$61.68 \$13,397.24
14 \$13,397.24 \$1,000.00 \$66.99 \$14,464.23
15 \$14,464.23 \$1,000.00 \$72.32 \$15,536.55
16 \$15,536.55 \$1,000.00 \$77.68 \$16,614.23
17 \$16,614.23 \$1,000.00 \$83.07 \$17,697.30
18 \$17,697.30 \$1,000.00 \$88.49 \$18,785.79
19 \$18,785.79 \$1,000.00 \$93.93 \$19,879.72
20 \$19,879.72 \$1,000.00 \$99.40 \$20,979.12
21 \$20,979.12 \$1,000.00 \$104.90 \$22,084.01
22 \$22,084.01 \$1,000.00 \$110.42 \$23,194.43
23 \$23,194.43 \$1,000.00 \$115.97 \$24,310.40
24 \$24,310.40 \$1,000.00 \$121.55 \$25,431.96
25 \$25,431.96 \$1,000.00 \$127.16 \$26,559.12
26 \$26,559.12 \$1,000.00 \$132.80 \$27,691.91
27 \$27,691.91 \$1,000.00 \$138.46 \$28,830.37
28 \$28,830.37 \$1,000.00 \$144.15 \$29,974.52
29 \$29,974.52 \$1,000.00 \$149.87 \$31,124.39
30 \$31,124.39 \$1,000.00 \$155.62 \$32,280.02
31 \$32,280.02 \$1,000.00 \$161.40 \$33,441.42
32 \$33,441.42 \$1,000.00 \$167.21 \$34,608.62
33 \$34,608.62 \$1,000.00 \$173.04 \$35,781.67
34 \$35,781.67 \$1,000.00 \$178.91 \$36,960.58
35 \$36,960.58 \$1,000.00 \$184.80 \$38,145.38
36 \$38,145.38 \$1,000.00 \$190.73 \$39,336.10
37 \$39,336.10 \$1,000.00 \$196.68 \$40,532.79
38 \$40,532.79 \$1,000.00 \$202.66 \$41,735.45
39 \$41,735.45 \$1,000.00 \$208.68 \$42,944.13
40 \$42,944.13 \$1,000.00 \$214.72 \$44,158.85
41 \$44,158.85 \$1,000.00 \$220.79 \$45,379.64
42 \$45,379.64 \$1,000.00 \$226.90 \$46,606.54
43 \$46,606.54 \$1,000.00 \$233.03 \$47,839.57
44 \$47,839.57 \$1,000.00 \$239.20 \$49,078.77
45 \$49,078.77 \$1,000.00 \$245.39 \$50,324.16
46 \$50,324.16 \$1,000.00 \$251.62 \$51,575.78
47 \$51,575.78 \$1,000.00 \$257.88 \$52,833.66
48 \$52,833.66 \$1,000.00 \$264.17 \$54,097.83
49 \$54,097.83 \$1,000.00 \$270.49 \$55,368.32
50 \$55,368.32 \$1,000.00 \$276.84 \$56,645.16
51 \$56,645.16 \$1,000.00 \$283.23 \$57,928.39
52 \$57,928.39 \$1,000.00 \$289.64 \$59,218.03
53 \$59,218.03 \$1,000.00 \$296.09 \$60,514.12
54 \$60,514.12 \$1,000.00 \$302.57 \$61,816.69
55 \$61,816.69 \$1,000.00 \$309.08 \$63,125.77
56 \$63,125.77 \$1,000.00 \$315.63 \$64,441.40
57 \$64,441.40 \$1,000.00 \$322.21 \$65,763.61
58 \$65,763.61 \$1,000.00 \$328.82 \$67,092.43
59 \$67,092.43 \$1,000.00 \$335.46 \$68,427.89
60 \$68,427.89 \$1,000.00 \$342.14 \$69,770.03

Case 2: Let’s use the same example with a single modification as the annuity is due:

Future Value of Due Annuity: \$70,118.88

Present Value: \$51,984.19

Interest: \$10,118.88

Annuity payments total value: \$60,000.00

Compound interest factor: 1.16865

The evolution per each period is presented below:

PeriodStarting balancePaymentInterestEnding Balance
1 \$0.00 \$1,000.00 \$5.00 \$1,005.00
2 \$1,005.00 \$1,000.00 \$10.03 \$2,015.03
3 \$2,015.03 \$1,000.00 \$15.08 \$3,030.10
4 \$3,030.10 \$1,000.00 \$20.15 \$4,050.25
5 \$4,050.25 \$1,000.00 \$25.25 \$5,075.50
6 \$5,075.50 \$1,000.00 \$30.38 \$6,105.88
7 \$6,105.88 \$1,000.00 \$35.53 \$7,141.41
8 \$7,141.41 \$1,000.00 \$40.71 \$8,182.12
9 \$8,182.12 \$1,000.00 \$45.91 \$9,228.03
10 \$9,228.03 \$1,000.00 \$51.14 \$10,279.17
11 \$10,279.17 \$1,000.00 \$56.40 \$11,335.56
12 \$11,335.56 \$1,000.00 \$61.68 \$12,397.24
13 \$12,397.24 \$1,000.00 \$66.99 \$13,464.23
14 \$13,464.23 \$1,000.00 \$72.32 \$14,536.55
15 \$14,536.55 \$1,000.00 \$77.68 \$15,614.23
16 \$15,614.23 \$1,000.00 \$83.07 \$16,697.30
17 \$16,697.30 \$1,000.00 \$88.49 \$17,785.79
18 \$17,785.79 \$1,000.00 \$93.93 \$18,879.72
19 \$18,879.72 \$1,000.00 \$99.40 \$19,979.12
20 \$19,979.12 \$1,000.00 \$104.90 \$21,084.01
21 \$21,084.01 \$1,000.00 \$110.42 \$22,194.43
22 \$22,194.43 \$1,000.00 \$115.97 \$23,310.40
23 \$23,310.40 \$1,000.00 \$121.55 \$24,431.96
24 \$24,431.96 \$1,000.00 \$127.16 \$25,559.12
25 \$25,559.12 \$1,000.00 \$132.80 \$26,691.91
26 \$26,691.91 \$1,000.00 \$138.46 \$27,830.37
27 \$27,830.37 \$1,000.00 \$144.15 \$28,974.52
28 \$28,974.52 \$1,000.00 \$149.87 \$30,124.39
29 \$30,124.39 \$1,000.00 \$155.62 \$31,280.02
30 \$31,280.02 \$1,000.00 \$161.40 \$32,441.42
31 \$32,441.42 \$1,000.00 \$167.21 \$33,608.62
32 \$33,608.62 \$1,000.00 \$173.04 \$34,781.67
33 \$34,781.67 \$1,000.00 \$178.91 \$35,960.58
34 \$35,960.58 \$1,000.00 \$184.80 \$37,145.38
35 \$37,145.38 \$1,000.00 \$190.73 \$38,336.10
36 \$38,336.10 \$1,000.00 \$196.68 \$39,532.79
37 \$39,532.79 \$1,000.00 \$202.66 \$40,735.45
38 \$40,735.45 \$1,000.00 \$208.68 \$41,944.13
39 \$41,944.13 \$1,000.00 \$214.72 \$43,158.85
40 \$43,158.85 \$1,000.00 \$220.79 \$44,379.64
41 \$44,379.64 \$1,000.00 \$226.90 \$45,606.54
42 \$45,606.54 \$1,000.00 \$233.03 \$46,839.57
43 \$46,839.57 \$1,000.00 \$239.20 \$48,078.77
44 \$48,078.77 \$1,000.00 \$245.39 \$49,324.16
45 \$49,324.16 \$1,000.00 \$251.62 \$50,575.78
46 \$50,575.78 \$1,000.00 \$257.88 \$51,833.66
47 \$51,833.66 \$1,000.00 \$264.17 \$53,097.83
48 \$53,097.83 \$1,000.00 \$270.49 \$54,368.32
49 \$54,368.32 \$1,000.00 \$276.84 \$55,645.16
50 \$55,645.16 \$1,000.00 \$283.23 \$56,928.39
51 \$56,928.39 \$1,000.00 \$289.64 \$58,218.03
52 \$58,218.03 \$1,000.00 \$296.09 \$59,514.12
53 \$59,514.12 \$1,000.00 \$302.57 \$60,816.69
54 \$60,816.69 \$1,000.00 \$309.08 \$62,125.77
55 \$62,125.77 \$1,000.00 \$315.63 \$63,441.40
56 \$63,441.40 \$1,000.00 \$322.21 \$64,763.61
57 \$64,763.61 \$1,000.00 \$328.82 \$66,092.43
58 \$66,092.43 \$1,000.00 \$335.46 \$67,427.89
59 \$67,427.89 \$1,000.00 \$342.14 \$68,770.03
60 \$68,770.03 \$1,000.00 \$348.85 \$70,118.88

17 Feb, 2015 | 0 comments