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FV of Annuity Due

Future value of beginning-of-period payments with periodic compounding.

When to use: Use for monthly or quarterly payments made at the beginning of each period.

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Formula

FVA=PMT×(1+km)n×m1km×(1+km)FVA = PMT \times \frac{\left(1 + \frac{k}{m}\right)^{n \times m} - 1}{\frac{k}{m}} \times \left(1 + \frac{k}{m}\right)

Variables

SymbolNameDescriptionUnit
FVAFuture Value of Annuity DueTotal future value of beginning-of-period payments$
PMTPaymentPeriodic payment amount (paid at start of period)$
kInterest RateNominal annual interest rate%
nNumber of YearsTime period in yearsyears
mCompounding FrequencyCompounding periods per yearinteger

Real-Life Examples

Example 1: Monthly Rent Savings

$1,200/month paid at start of month, earning 6% monthly compounding for 5 years.

Given

PMT = 1,200k = 0.06n = 5m = 12

Step-by-Step

1.FVA = $1,200 × [(1.005)^60 - 1] / 0.005 × 1.005
2.FVA = $1,200 × 69.7700 × 1.005
3.FVA = $1,200 × 70.1189
4.FVA = $84,142.69
Result:84,142.69

Monthly beginning-of-period savings total $84,142.69.

Example 2: Quarterly Dues

$2,500/quarter paid at start, 8% quarterly compounding for 10 years.

Given

PMT = 2,500k = 0.08n = 10m = 4

Step-by-Step

1.FVA = $2,500 × [(1.02)^40 - 1] / 0.02 × 1.02
2.FVA = $2,500 × 60.4020 × 1.02
3.FVA = $2,500 × 61.6100
4.FVA = $154,025.01
Result:154,025.01

Quarterly beginning-of-period payments accumulate to $154,025.01.

Frequently Asked Questions

Use this formula with m=12 for monthly payments. Enter the monthly deposit as PMT, annual rate as k, years as n, and 12 as m. The formula accounts for each deposit earning interest from the start of the month.

Both use the same periodic rate (k/m), but the annuity due multiplies the result by (1 + k/m) to account for each payment earning one extra period of interest since payments are made at the beginning rather than the end of each period.

The impact of beginning-of-period vs. end-of-period timing grows with higher interest rates and longer time horizons. For small amounts over short periods at low rates, the difference may be modest, but over decades it can add up to thousands of dollars.