## The time value of money

### 1. The dollar and time

Look at the following data:

Year | 1963 | 2009 |
---|---|---|

New honours graduate salary | $800 per year | $50,000 per year |

3 bedroom house | $2,825 | $400,000 |

Small car | $400 | $10,000 |

All monies are in dollars, but they clearly do not have the same value. The $ in 1963 was worth more than the one today. So a $ today is worth more than a $ tomorrow; a demonstration of the time value of money.

This approach is general, not specific or numerate. That is where discount tables come in.

### 2. Discount tables

Imagine that you invest $100 at 10% per annum, compounded annually. Your deposit would grow.

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Value | 100 | 110 | 121 | 133 | 146 | 160 | 176 |

This is the future value of a $ today at 10%. We can turn this round and look at the present value of a $ earned in the future. It is the reciprocal of the numbers above.

Present value of $1 earned in the future.

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Present value | 1.000 | 0.909 | 0.826 | 0.75 | 0.684 | 0.625 | 0.568 |

This tells us that a $ received in 3 years time is worth the same as 75 cents today at 10% rate of interest.

Do the same thing for an interest rate of 20% and we get:

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Future value | 100 | 120 | 144 | 173 | 207 | 249 | 299 |

Present value | 1.000 | 0.833 | 0.694 | 0.578 | 0.483 | 0.401 | 0.334 |

The higher the interest rate, the less money is worth received in the future.

For interest rate, read discount rate and you have the discount tables.