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Ordinary Annuity

4 formulas

Ordinary annuity formulas value a series of equal payments made at the end of each period. Common applications include loan payments, bond coupon payments, and retirement savings contributions. The key distinction is that payments occur at the end of each compounding period.

FV of Ordinary Annuity

Calculates the future value of a series of equal end-of-year payments.

FVA=PMT×(1+k)n−1kFVA = PMT \times \frac{(1 + k)^n - 1}{k}

Showing annual compounding

3 compounding options

PV of Ordinary Annuity

Calculates the present value of a series of equal end-of-year payments.

PVA=PMT×1−(1+k)−nkPVA = PMT \times \frac{1 - (1 + k)^{-n}}{k}

Showing annual compounding

3 compounding options

Payment from PV

Calculates the periodic payment needed to pay off a present value over n periods.

PMT=PV×k1−(1+k)−nPMT = PV \times \frac{k}{1 - (1 + k)^{-n}}

Showing annual compounding

3 compounding options

Payment from FV

Calculates the periodic payment needed to reach a future value goal.

PMT=FV×k(1+k)n−1PMT = FV \times \frac{k}{(1 + k)^n - 1}

Showing annual compounding

3 compounding options