Level 7: Growth, decay and annuities

Ratio, rates and money · level 7 of 8 · rough age 15-16 (a guide for parents; anyone can start anywhere)

In level 6 you multiplied by the same percent again and again. In this level that one idea describes populations, medicines, cooling drinks and radioactive atoms, and you learn to measure it by doubling times and half-lives. Then you take money seriously across time: compounding monthly or daily, the present value of a future amount, and annuities, the streams of regular payments behind every savings plan and loan, added up as geometric series. The level ends with the numbers of a whole financial life: tax brackets, pay cheques, budgets and net worth.

Lesson	You will be able to
Exponential growth and decay in the world	Model a quantity with a growth or decay factor, spot exponential data, and explain why populations, medicines and cooling behave this way
Doubling time and half-life	Find doubling times and half-lives exactly with logarithms, date with carbon-14, and explain why the rule of 72 works and when it fails
Compounding periods	Use the rate per period, compare offers by their effective annual rates, and convert between compounding periods
Present value	Find how much to invest now for a future goal, compare money at different times, and solve for a rate or a time
Annuities	Derive and use the future value of regular deposits as a geometric series, and find the deposit needed for a goal
Present value of an annuity	Value a stream of payments today, find a loan's payment and total interest, and price a perpetuity
Planning a financial life	Tell marginal from average tax rates, read a pay cheque, plan an emergency fund and work out net worth

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