## Self-Check Questions

Table shows the fruit prices that the typical college student purchased from 2001 to 2004. What is the amount spent each year on the “basket” of fruit with the quantities shown in column 2?

Items | Qty | (2001) Price | (2001) Amount Spent | (2002) Price | (2002) Amount Spent | (2003) Price | (2003) Amount Spent | (2004) Price | (2004) Amount Spent |
---|---|---|---|---|---|---|---|---|---|

Apples | 10 | $0.50 | $0.75 | $0.85 | $0.88 | ||||

Bananas | 12 | $0.20 | $0.25 | $0.25 | $0.29 | ||||

Grapes | 2 | $0.65 | $0.70 | $0.90 | $0.95 | ||||

Raspberries | 1 | $2.00 | $1.90 | $2.05 | $2.13 | $2.13 | |||

Total |

## Hint:

To compute the amount spent on each fruit in each year, you multiply the quantity of each fruit by the price.

- 10 apples × 50 cents each = $5.00 spent on apples in 2001.
- 12 bananas × 20 cents each = $2.40 spent on bananas in 2001.
- 2 bunches of grapes at 65 cents each = $1.30 spent on grapes in 2001.
- 1 pint of raspberries at $2 each = $2.00 spent on raspberries in 2001.

Adding up the amounts gives you the total cost of the fruit basket. The total cost of the fruit basket in 2001 was $5.00 + $2.40 + $1.30 + $2.00 = $10.70. The total costs for all the years are shown in the following table.

2001 | 2002 | 2003 | 2004 |
---|---|---|---|

$10.70 | $13.80 | $15.35 | $16.31 |

Construct the price index for a “fruit basket” in each year using 2003 as the base year.

## Hint:

If 2003 is the base year, then the index number has a value of 100 in 2003. To transform the cost of a fruit basket each year, we divide each year’s value by $15.35, the value of the base year, and then multiply the result by 100. The price index is shown in the following table.

2001 | 2002 | 2003 | 2004 |
---|---|---|---|

69.71 | 89.90 | 100.00 | 106.3 |

Note that the base year has a value of 100; years before the base year have values less than 100; and years after have values more than 100.

Compute the inflation rate for fruit prices from 2001 to 2004.

## Hint:

The inflation rate is calculated as the percentage change in the price index from year to year. For example, the inflation rate between 2001 and 2002 is (84.61 – 69.71) / 69.71 = 0.2137 = 21.37%. The inflation rates for all the years are shown in the last row of the following table, which includes the two previous answers.

Items | Qty | (2001) Price | (2001) Amount Spent | (2002) Price | (2002) Amount Spent | (2003) Price | (2003) Amount Spent | (2004) Price | (2004) Amount Spent |
---|---|---|---|---|---|---|---|---|---|

Apples | 10 | $0.50 | $5.00 | $0.75 | $7.50 | $0.85 | $8.50 | $0.88 | $8.80 |

Bananas | 12 | $0.20 | $2.40 | $0.25 | $3.00 | $0.25 | $3.00 | $0.29 | $3.48 |

Grapes | 2 | $0.65 | $1.30 | $0.70 | $1.40 | $0.90 | $1.80 | $0.95 | $1.90 |

Raspberries | 1 | $2.00 | $2.00 | $1.90 | $1.90 | $2.05 | $2.05 | $2.13 | $2.13 |

Total | $10.70 | $13.80 | $15.35 | $16.31 | |||||

Price Index | 69.71 | 84.61 | 100.00 | 106.3 | |||||

Inflation Rate | 21.37% | 18.19% | 6.3% |

Edna is living in a retirement home where most of her needs are taken care of, but she has some discretionary spending. Based on the basket of goods in Table, by what percentage does Edna’s cost of living increase between time 1 and time 2?

Items | Quantity | (Time 1) Price | (Time 2) Price |
---|---|---|---|

Gifts for grandchildren | 12 | $50 | $60 |

Pizza delivery | 24 | $15 | $16 |

Blouses | 6 | $60 | $50 |

Vacation trips | 2 | $400 | $420 |

## Hint:

Begin by calculating the total cost of buying the basket in each time period, as shown in the following table.

Items | Quantity | (Time 1) Price | (Time 1) Total Cost | (Time 2) Price | (Time 2) Total Cost |
---|---|---|---|---|---|

Gifts | 12 | $50 | $600 | $60 | $720 |

Pizza | 24 | $15 | $360 | $16 | $384 |

Blouses | 6 | $60 | $360 | $50 | $300 |

Trips | 2 | $400 | $800 | $420 | $840 |

Total Cost | $2,120 | $2,244 |

The rise in cost of living is calculated as the percentage increase:

(2244 – 2120) / 2120 = 0.0585 = 5.85%.