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FV of Growing Annuity Due

Future value of growing beginning-of-period payments.

When to use: Use when growing deposits are made at the start of each period.

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Formula

FVA=PMTkg×[(1+k)n(1+g)n]×(1+k)FVA = \frac{PMT}{k - g} \times \left[(1 + k)^n - (1 + g)^n\right] \times (1 + k)

Variables

SymbolNameDescriptionUnit
FVAFuture Value of AnnuityAccumulated value$
PMTFirst PaymentThe first payment amount$
kInterest RateRate of return%
gGrowth RatePayment growth rate%
nNumber of YearsNumber of periodsyears

Real-Life Examples

Example 1: Growing Savings Due

$4,000 first year, growing 2%/year, deposited at start of year, 7% return for 25 years.

Given

PMT = 4,000k = 0.07g = 0.02n = 25

Step-by-Step

1.FVA = ($4,000 / 0.05) × [(1.07)^25 - (1.02)^25] × 1.07
2.FVA = $80,000 × [5.4274 - 1.6406] × 1.07
3.FVA = $80,000 × 3.7868 × 1.07
4.FVA = $80,000 × 4.0519
5.FVA = $324,149.38
Result:324,149.38

Growing beginning-of-year deposits accumulate to $324,149.38.

Example 2: Growing Rent Invested

Rental income starts at $18,000/year, grows 3%/year, invested at start of year at 9% for 15 years.

Given

PMT = 18,000k = 0.09g = 0.03n = 15

Step-by-Step

1.FVA = ($18,000 / 0.06) × [(1.09)^15 - (1.03)^15] × 1.09
2.FVA = $300,000 × [3.6425 - 1.5580] × 1.09
3.FVA = $300,000 × 2.0845 × 1.09
4.FVA = $300,000 × 2.2721
5.FVA = $681,632.89
Result:681,632.89

Growing rent deposits accumulate to $681,632.89.

Frequently Asked Questions

The annuity due version multiplies the result by (1 + k), reflecting the extra period of growth each beginning-of-period payment receives. This produces a higher future value compared to end-of-period payments.

Use it when you make increasing contributions at the start of each period — like beginning-of-year retirement deposits that grow annually with your salary. The formula captures both the payment growth and the early-deposit timing advantage.

The difference is the ordinary growing annuity FVA multiplied by the periodic rate. At typical rates (6-8%) over 20-30 years, beginning-of-period timing adds roughly 6-8% more to the final accumulated balance.