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Present Value of Annuity

An annuity is a series of payments made at equal intervals. The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the fact that payments are being made at various moments in the future.

The present value of an annuity depends on the value of periodic payments multiplied by the discounted interest compounded over the number of payments, accounting for the frequency of payments and any growth in the periodic payments.

Formula

QuantityVariable["PV", "Money"] == ((1 - ((1 + QuantityVariable["g", "Unitless"])/(1 + QuantityVariable["i", "Unitless"]/QuantityVariable["f", "Unitless"]))^(QuantityVariable["f", "Unitless"]*QuantityVariable["n", "Unitless"]))*QuantityVariable["PMT", "Money"])/(-QuantityVariable["g", "Unitless"] + QuantityVariable["i", "Unitless"]/QuantityVariable["f", "Unitless"])

symbol description physical quantity
PV present value "Money"
g periodic payment growth rate "Unitless"
f payments per period "Unitless"
i interest rate "Unitless"
n number of periods "Unitless"
PMT periodic payment "Money"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Present Value of Annuity"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Present Value of Annuity"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Present Value of Annuity"], {QuantityVariable["n","Unitless"] -> 4, QuantityVariable["i","Unitless"] -> Quantity[8, "Percent"], QuantityVariable["PMT","Money"] -> Quantity[1000, "USDollars"]}]
Out[3]=

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