What happens when you invest $£1\; 000 \;000$ at $4 \%$? [You could use this spreadsheet to investigate.]

How long does it take to double the money?

What would happen if we begin to spend money, withdrawing it at the start of each year? You might like to look at this spreadsheet and think about the following:

- Why do you think the interest for the first year isn't £40000?
- Extend the spreadsheet further and, by changing the yearly expenditure, experiment with trying to make the balance each year settle at around £980,000 or giving the £1,000,000 a lifetime of $20$ years.

What happens if you take account of inflation when thinking
about how much you might spend each year? This spreadsheet might be
useful for investigating this idea. You might like to think about
some of the following:

- What is the interest rate in this spreadsheet?
- What is the inflation rate?
- What annual expenditure would leave no (or a very small) balance left at the end of $50$ years? What is the total income/expinditure at the end of $50$ years in this case?
- What interest rates and inflation rates would guarantee an income of £3000000 if you spent the same amount each year (taking into account inflation), with only a small balance, or no balance, at the end?