The Legacy

You have been left one million pounds! How to spend or invest it over 50 years?

Author: Dundee City UK

Topic: Mathematics

Tags Interest, Tables, Modelling

This activity originates from a problem posed on the NRICH website. (

Your school has been left £1,000,000 in the will of an ex-pupil but there are conditions:

  • the school must benefit by spending part of the money every year,
  • the investment should have a lifetime of at least 50 

There are various possible models of investment and expenditure based on any balance being invested at a fixed interest/inflation rate. What model would you choose to ensure the best return for the school over a period of 50 years?

This is an opportunity to investigate what happens when variables such as interest, inflation rates and how much is spent each year are changed. Investigating how a small change in interest rates can affect the total income over different time periods can be enlightening. Investigating the impact of spending large amounts of money up-front can also provide valuable insights.

Five different models are provided in a tns file and students can explore the effect for example of changing inflation rates, of spending large amounts of money early etc.

A 3-page student handout is provided, and there are teacher notes to accompany the TI-Nspire document.