Sunday, 17 November 2013

Insurance Benefits - Endowment

Pure Endowment

An Endowment benefit is just a Term benefit (as calculated in the previous post) plus a Pure Endowment of 1. This is defined as:


Yearly and Quarterly Benefits

 Thus for yearly and quarterly benefits we can use a simple addition to the Term function. We first need to create a function to calculate the npx value:

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open System.Collections.Generic
/// npx generated for book referencing Makehams formula
let rec book_npx x n = 
    let A = 0.00022
    let B = 0.0000027
    let c = 1.124
    //calculate result
    makeham_tpx A B c x n
/// Endowment Axn using memoized version of Ax1n 
let Axn x n = (mem_Ax1n x n) + (book_npx x n)/1.05**n
/// Endowment quarterly Axn using memoized version of quarterly Ax1n 
let Axn_4 x n = (mem_Ax1n4 x n) + (book_npx x n)/1.05**n

We can then use FCell to reference these functions to get a grid of values in Excel:

These are the same values as on page 91 of the book.

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