Pure EndowmentAn 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 BenefitsThus 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:
1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12:
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.