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## 'The Legacy' printed from http://nrich.maths.org/

This is an opportunity for pupils to set up their own models using
a spreadsheet and investigate what happens when they change
variables such as interest, inflation rates and how much is spent
each year. 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.

Some models are suggested on the model cards which have varying
levels of complexity. Some suggestions about how a series of
sessions working on this problem might run are given briefly
below.

After spending some time "making sense" of the problem and what is
meant by a model, discuss ideas for making good use of the legacy:

- What types of things should the money be spent on?
- Why would the ex-pupil want the money to have a long term
impact?
- What is the importance of inflation in any model we try?
- Why would you invest the money?

Students could work in groups to think about the models they
might like to investigate then choose two models to compare. Think
about:

- Total expenditure for each model,
- Benefits and limitations of each model,
- Comparisons between models,
- How a change in inflation might change the
recommendations,
- How a change in the time-scale for using the money might affect
any recommendation.

A plenary might include a discussion of the elegance or
realism of some of the models and what the use of a spreadsheet had
to offer to the task.