Introduction to Financial Mathematics

Agenda

• What is Interest?
• Present Value and Future Value
• Practice

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1.

What is Interest?

Is this interesting?

What is Interest?

• Consider $100
• If left in a box for 1 year, how much should be there?

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What is Interest?

• Consider $100
• If left in a box for 1 year, how much should be there?
• $100

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What is Interest?

• Consider $100
• If left in a box for 1 year, how much should be there?
• $100
• Suppose the $100 is given to someone else with a promise of payment at the end of the year
• The difference between the $100 and what is actually paid back is called the interest

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What is Interest?

• Ideally, if you are the lender:
• Interest is positive and large
• Ideally, if you are the lendee:
• Interest is either positive and small, or;
• Interest is negative

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International Mindedness

Different societies view borrowing and lending of money differently. How is it viewed in your culture?

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Indigenous Groups

Many indigenous communities traditionally used interest-free lending based on reciprocity and community support:

• Rotating savings groups (like African "susu" or Mexican "tanda")
• Community-based lending with social rather than financial returns
• Gift economies (helping others→ social obligation rather than financial debt)

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Types of Interest

• If the payment is in a single transaction
• Simple interest is the fee for the loan, usually expressed as a percentage
• The interest is only ever calculated on the principal

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Types of Interest

• Most of the time, the payment is across multiple transactions
• Compound interest is calculated on the current total, including past interest
• This is a geometric sequence

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Compound Interest Calculations

• Given principal P, interest rate i, number of calculations n

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• May need to adjust time units accordingly
• Always draw a timeline!

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2.

Present Value and Future Value

When do we compute?

Present Value and Future Value

• When comparing money values, the amounts must always be adjusted to the same point in time
• Ex - consider cost of inflation
• Present Value is the value now
• Future Value is the value later
• You may need to adjust two different values to a common point in the past or future - use compound interest formula

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3.

Practice

We want to practice everything!

Practice

• See the examples

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Credits

Special thanks to all the people who made and released these awesome resources for free:

• Presentation template by SlidesCarnival

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