accumulatedValue: Function to evaluate the accumulated value.

In lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

Function to evaluate the accumulated value.

Description

This function returns the value at time n of a series of equally spaced payments of 1.

Usage

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

Arguments

i	Effective interest rate expressed in decimal form. E.g. 0.03 means 3%.
n	Number of terms of payment.
m	Deferring period, whose default value is zero.
k	Frequency of payment.
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

The accumulated value is the future value of the terms of an annuity. Its mathematical expression is s_{\left. {\overline {\, n \,}}\! \right| } = {\left( {1 + i} \right)^n} a_{\left. {\overline {\, n \,}}\! \right| }. The payment timing follows the type argument: an annuity-immediate has payments at the end of each period, while an annuity-due has payments at the beginning of each period.

Value

A numeric value representing the calculated accumulated value.

Warning

The function is provided as is, without any guarantee regarding the accuracy of calculation. We disclaim any liability for eventual losses arising from direct or indirect use of this software.

Note

Accumulated values are derived from annuities by the following basic equation {s_{\left. {\overline {\, n \,}}\! \right| }} = {\left( {1 + i} \right)^n} = a_{\left. {\overline {\, n \,}}\! \right| }.

Author(s)

Giorgio A. Spedicato

References

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

See Also

annuity

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