# accumulatedValue: Function to evaluate the accumulated value. In spedygiorgio/lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

## Description

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

## Usage

 1  accumulatedValue(i, n,m=0, k,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, either "advance" for the annuity due (default) or "arrears" for the annuity immediate. Alternatively, one can use "due" or "immediate" respectively (can be abbreviated).

## Details

The accumulated value is the future value of the terms of an annuity. Its mathematical expression is s_{≤ft. {\overline {\, n \,}}\! \right| } = ≤ft( {1 + i} \right)^n a_{≤ft. {\overline {\, n \,}}\! \right| }

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

## Author(s)

Giorgio A. Spedicato

## References

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

annuity
 1 2 3 4 5 6 #A man wants to save 100,000 to pay for his sons #education in 10 years time. An education fund requires the investors to #deposit equal installments annually at the end of each year. If interest of #0.075 is paid, how much does the man need to save each year in order to #meet his target? R=100000/accumulatedValue(i=0.075,n=10)