This present value of growing annuity calculator estimates the value in today’s money of a growing future payments series for a no. of periods the interest is compounded (due or ordinary annuity). There is more information on how to calculate this financial figure below the form.

Payment amount:*
\$
Payment growing rate per period:
%
Interest rate per period:*
%
Number of time periods:*
Annuity type:*

## How does this present value of growing annuity calculator work?

This tool can help you figure out the present value of a series of future growing annuity payments, either ordinary (made at the end of each period) or due (at each period’s beginning) by considering these figures:

• Starting payment amount you expect to receive/pay at the 1st period.
• Payment growing rate per period meaning a percentage you expect that your regular payment will increase from one period to the next.
• Interest rate per periodwhich is a fixed percent (most often referred to as yearly) representing the cost for the money use.
• Number of time periods is the time frame in which the interest is compounded (year, twice a year, month.) and by convention this should refer to the same time period as the interest rate. For example if the interest is considered on an monthly basis, then the Number of periods by default will be expressed in months.
• Present Value of Growing Annuity (PVGOA or PVGDA) is calculated depending on the annuity type

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

• In ordinary case the formula is:

- If Interest rate per period ≠ Growing payment rate then:

[PVGOA] = PA/(r – gr) * [1 – (((1 + gr)/(1 + r))^NP)]

- If Interest rate per period = Growing payment rate then:

[PVGOA] = PA * NP/(1 + r)

• In due case the equation is:

[PVGDA] = PVGOA * (1 + r)

• Interest [B] = [FV] – [VP]

• Regular payments total value [VP] = RP * NP

• Future Value [FV] = (PVGOA or PVGDA) * [(1 + r)^NP]

• Compound interest factor [C] = 1 + ([B]/[VP])

Where:

PA = Payment amount

FV = Future value

NP = Number of time periods

r = Interest rate per period

gr = Growing payment rate

Moreover, together with the indicators explained above this calculator also returns a detailed schedule showing the exact evolution of the annuities per each period.

## Example of 3 results

Scenario 1: Let’s choose an ordinary annuity with an initial payment of \$1,000, growing by 10% per each year over the next 15 years, while the annual interest rate is assumed to be 4.25%. This will result in:

Present Value of Growing Ordinary Annuity: \$21,520.51

Interest: \$8,406.00

Payments total value: \$31,772.48

Future Value: \$40,178.48

Compound interest factor: 1.26457

The evolution of the present value of growing annuity per each period is presented below:

PeriodStarting balancePaymentInterestEnding Balance
1 \$0.00 \$1,000.00 \$0.00 \$1,000.00
2 \$1,000.00 \$1,100.00 \$42.50 \$2,142.50
3 \$2,142.50 \$1,210.00 \$91.06 \$3,443.56
4 \$3,443.56 \$1,331.00 \$146.35 \$4,920.91
5 \$4,920.91 \$1,464.10 \$209.14 \$6,594.15
6 \$6,594.15 \$1,610.51 \$280.25 \$8,484.91
7 \$8,484.91 \$1,771.56 \$360.61 \$10,617.08
8 \$10,617.08 \$1,948.72 \$451.23 \$13,017.02
9 \$13,017.02 \$2,143.59 \$553.22 \$15,713.83
10 \$15,713.83 \$2,357.95 \$667.84 \$18,739.62
11 \$18,739.62 \$2,593.74 \$796.43 \$22,129.79
12 \$22,129.79 \$2,853.12 \$940.52 \$25,923.43
13 \$25,923.43 \$3,138.43 \$1,101.75 \$30,163.60
14 \$30,163.60 \$3,452.27 \$1,281.95 \$34,897.82
15 \$34,897.82 \$3,797.50 \$1,483.16 \$40,178.48

Scenario 2: Let’s assume a due annuity similar to the one given above and compare the difference in figures:

Present Value of Growing Due Annuity: \$22,435.13

Interest: \$10,113.58

Payments total value: \$31,772.48

Future Value: \$41,886.07

Compound interest factor: 1.31831

The evolution of the present value of growing annuity per each period is presented below:

PeriodStarting balancePaymentInterestEnding Balance
1 \$0.00 \$1,000.00 \$42.50 \$1,042.50
2 \$1,042.50 \$1,100.00 \$91.06 \$2,233.56
3 \$2,233.56 \$1,210.00 \$146.35 \$3,589.91
4 \$3,589.91 \$1,331.00 \$209.14 \$5,130.05
5 \$5,130.05 \$1,464.10 \$280.25 \$6,874.40
6 \$6,874.40 \$1,610.51 \$360.61 \$8,845.52
7 \$8,845.52 \$1,771.56 \$451.23 \$11,068.30
8 \$11,068.30 \$1,948.72 \$553.22 \$13,570.24
9 \$13,570.24 \$2,143.59 \$667.84 \$16,381.67
10 \$16,381.67 \$2,357.95 \$796.43 \$19,536.05
11 \$19,536.05 \$2,593.74 \$940.52 \$23,070.31
12 \$23,070.31 \$2,853.12 \$1,101.75 \$27,025.17
13 \$27,025.17 \$3,138.43 \$1,281.95 \$31,445.55
14 \$31,445.55 \$3,452.27 \$1,483.16 \$36,380.98
15 \$36,380.98 \$3,797.50 \$1,707.59 \$41,886.07

Scenario 3: Let’s assume an ordinary annuity similar to the one from the 1st scenario, with two changes: both the interest rate and the growing rate are considered to be equal to 5%:

Present Value of Growing Due Annuity: \$15,000.00

Interest: \$9,605.36

Payments total value: \$21,578.56

Future Value: \$31,183.92

Compound interest factor: 1.44513

The evolution of the present value of growing annuity per each period is presented below:

PeriodStarting balancePaymentInterestEnding Balance
1 \$0.00 \$1,000.00 \$50.00 \$1,050.00
2 \$1,050.00 \$1,050.00 \$105.00 \$2,205.00
3 \$2,205.00 \$1,102.50 \$165.38 \$3,472.88
4 \$3,472.88 \$1,157.63 \$231.53 \$4,862.03
5 \$4,862.03 \$1,215.51 \$303.88 \$6,381.41
6 \$6,381.41 \$1,276.28 \$382.88 \$8,040.57
7 \$8,040.57 \$1,340.10 \$469.03 \$9,849.70
8 \$9,849.70 \$1,407.10 \$562.84 \$11,819.64
9 \$11,819.64 \$1,477.46 \$664.85 \$13,961.95
10 \$13,961.95 \$1,551.33 \$775.66 \$16,288.95
11 \$16,288.95 \$1,628.89 \$895.89 \$18,813.73
12 \$18,813.73 \$1,710.34 \$1,026.20 \$21,550.28
13 \$21,550.28 \$1,795.86 \$1,167.31 \$24,513.44
14 \$24,513.44 \$1,885.65 \$1,319.95 \$27,719.04
15 \$27,719.04 \$1,979.93 \$1,484.95 \$31,183.92

12 Feb, 2015 | 0 comments