# Film Series Three: Mathematics of Finance and Growth

In this series of films we examine many circumstances where it is crucial to understand what is happening over a substantial time period. Individuals sometimes have to save for some while in order to finance large expenditures. How quickly do savings grow if the money is saved? Businesses frequently take decisions on whether it is worth borrowing in order to refurbish or expand. Sometimes people are not incurring debt but trying to get out of it. How do people pay back to banks and building societies the large sums they have borrowed to buy a house? We see how the mathematics of finance can help give an insight into these questions.

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#### 3.01 Compound Interest - Establishing a Formula

In this example we meet a student who is saving for a round-the-world trip and we derive a formula to calculate how long this will take. (7 minutes 50 seconds).

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| Related MathsEG materialDiscrete compound interest |

#### 3.02 Compound Interest - Building Up Personal Savings

Using the formula we derived in the previous film we now calculate how long it will take for this student's money to grow so that she can afford to take her round-the-world trip. (4 minutes 25 seconds).

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| Related MathsEG materialDiscrete compound interest |

#### 3.03 Compound Growth Rates in an Austrian Health Spa

Bad Blumau is a remarkable health and fitness spa 40 miles from Vienna. In this example we assume that managers wish to add a new service at the spa that will cost 100,000 Euro to establish. Assuming an increase in visitor numbers attracted by the new service, how long will it take for the investment to be recovered? (8 minutes 14 seconds).

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| Related MathsEG materialContinuous compound interest |

#### 3.04 Geometric Series - Clearing a Mortgage Debt

The couple in this example would like to buy a house but need a mortgage. We use geometric series to calculate their monthly payments over 25 years. (8 minutes 24 seconds).

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| Related MathsEG materialDiscrete compound interest |

#### 3.05 The Mathematics of Finance - Understanding DCF Techniques

In this section we look at decisions to invest and derive the formula for calculating Discounted Cash Flow. This helps us address such questions as whether it is financially worthwhile getting a degree, or if a company should spend money on capital investment. Will what they get back in sales, or in cost savings, justify the expenditure? (8 minutes 1 second).

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| Related MathsEG materialPV, NPV & IRR |

#### 3.06 Discounted Cash Flow - Investing in Education

Using our formula we determine whether an investment in education is worthwhile. (7 minutes 10 seconds).

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| Related MathsEG materialPV, NPV & IRR |

#### 3.07 DCF - Europa Food's Decision to Save Labour Costs

In the South of England a farmer is facing similar questions about investment. Agriculture in the UK and elsewhere is facing severe shortages of labour and farmers are struggling with investment decisions to reduce their reliance on labour. One option for this farmer is robotics and automation. (13 minutes 1 second).

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#### 3.08 Eurotunnel - A Bad Investment

Sometimes investment decisions go spectacularly wrong. For example, the private investors who funded the Eurotunnel project lost nearly all their money. In this case the mathematics was correct, but this film shows how its value as a tool for making investment decisions depends on the accuracy of the forecast data that is processed. (3 minutes 51 seconds).

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| Related MathsEG materialSinking funds, annuities & perpetuities |

#### 3.09 Geometric Series - Changes Over Time in a Country's Living Standards

Here we move away from the mathematics of finance to the mathematics of economics to examine the relationship between income and population growth. Does an increasing population mean that standards of living will decline over time? (4 minutes 27 seconds).

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| Related MathsEG materialGrowth & decay |

#### 3.10 Geometric Progression - Growth in European Economies

Of the ten countries that joined the EU in 2004 Poland has the largest economy. However, its average income is only around 9,500 Euro p.a. If Poland can sustain a growth rate of around five per cent for some time it can hope to reach the EU average eventually. How long will it be? (7 minutes 44 seconds).

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| Related MathsEG materialContinuous compound interest |

#### 3.11 Geometric Progression - How long will the World's oil stocks last?

It is possible to apply the principles learned in the earlier film to positive or negative growth in any variable. We extend our analysis to examine global stocks of oil and ask how long it will be before the stocks are depleted. (6 minutes 9 seconds).

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| Related MathsEG materialSinking funds, annuities & perpetuities |

#### 3.12 Conclusion

A summary of what has been learned in film series three. (44 seconds).

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| Related MathsEG materialSinking funds, annuities & perpetuities |