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 |
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.
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 (89.90 – 69.71) / 69.71 = 0.2137 = 28.96%. 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 | 89.90 | 100.00 | 106.3 | |||||
| Inflation Rate | 28.96% | 11.23% | 6.3% |
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%.
Since the CPI measures the prices of the goods and services purchased by the typical urban consumer, it measures the prices of things that people buy with their paycheck. For that reason, the CPI would be the best price index to use for this purpose.
The PPI is subject to those biases for essentially the same reasons as the CPI is. The GDP deflator picks up prices of what is actually purchased that year, so there are no biases. That is the advantage of using the GDP deflator over the CPI.
The calculator requires you to input three numbers:
- The first year, in this case the year of your birth
- The amount of money you would want to translate in terms of its purchasing power
- The last year—now or the most recent year the calculator will accept
My birth year is 1955. The amount is $1. The year 2012 is currently the latest year the calculator will accept. The simple purchasing power calculator shows that $1 of purchases in 1955 would cost $8.57 in 2012. The website also explains how the true answer is more complicated than that shown by the simple purchasing power calculator.
The state government would benefit because it would repay the loan in less valuable dollars than it borrowed. Plus, tax revenues for the state government would increase because of the inflation.
Higher inflation reduces real interest rates on fixed rate mortgages. Because ARMs can be adjusted, higher inflation leads to higher interest rates on ARMs.
Because the mortgage has an adjustable rate, the rate should fall by 3%, the same as inflation, to keep the real interest rate the same.