annuity: Annuity

In lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

Annuity

Description

This function calculates the present value of a stream of fixed payments separated by equal intervals of time.

Usage

annuity(i, n, m = 0, k = 1, type = "immediate")

Arguments

i	Effective interest rate expressed in decimal form. E.g. 0.03 means 3%. It can be a vector of interest rates of the same length of periods.
n	Periods for payments. If n = infinity then annuity returns the value of a perpetuity (either immediate or due).
m	Deferring period, whose default value is zero.
k	Yearly payments frequency. A payment of k^-1 is supposed to be performed at the end of each year.
type	The payment type. Use "immediate" (default) for an annuity-immediate, where payments are made at the end of each period, or "due" for an annuity-due, where payments are made at the beginning of each period. For compatibility, "arrears" is an alias for "immediate" and "advance" is an alias for "due" (can be abbreviated).

Details

For an annuity-immediate the first payment occurs at time 1/k; for an annuity-due the first payment occurs at time 0. Thus, for annual payments, an annuity-immediate has payment times 1,2,\ldots,n, whereas an annuity-due has payment times 0,1,\ldots,n-1.

Value

A numeric value representing the present value of the annuity.

Note

The value returned by annuity function derives from direct calculation of the discounted cash flow and not from formulas, like {a^{\left( m \right)}}_{\left. {\overline {\, n \,}}\! \right| } = \frac{{1 - {v^n}}}{{{i^{\left( m \right)}}}}. When m is greater than 1, the payment per period is assumed to be \frac{1}{m}.

Author(s)

Giorgio A. Spedicato

References

Broverman, S.A., Mathematics of Investment and Credit (Fourth Edition), 2008, ACTEX Publications.

lifecontingencies documentation built on Aug. 24, 2026, 1:07 a.m.