To determine which case had an inflation rate of 12 percent over the last year, we can use the formula for calculating the inflation rate based on the price index. The formula is:
\[ \text{Inflation Rate} = \left( \frac{\text{Current Price Index} - \text{Previous Price Index}}{\text{Previous Price Index}} \right) \times 100 \]
Now let's apply this formula to each of the options:
a.
- Previous Price Index = 110
- Current Price Index = 120
\[ \text{Inflation Rate} = \left( \frac{120 - 110}{110} \right) \times 100 = \left( \frac{10}{110} \right) \times 100 \approx 9.09% \]
b.
- Previous Price Index = 145
- Current Price Index = 163
\[ \text{Inflation Rate} = \left( \frac{163 - 145}{145} \right) \times 100 = \left( \frac{18}{145} \right) \times 100 \approx 12.41% \]
c.
- Previous Price Index = 134
- Current Price Index = 150
\[ \text{Inflation Rate} = \left( \frac{150 - 134}{134} \right) \times 100 = \left( \frac{16}{134} \right) \times 100 \approx 11.94% \]
d.
- Previous Price Index = 120
- Current Price Index = 132
\[ \text{Inflation Rate} = \left( \frac{132 - 120}{120} \right) \times 100 = \left( \frac{12}{120} \right) \times 100 = 10% \]
Conclusion:
Among the options:
- Case b had an inflation rate of approximately 12.41%.
- Case c had an inflation rate of approximately 11.94%, which is close to 12% but not exact.
Thus, case b is the only option where the inflation rate (12.41%) is closest to 12%, considering rounding.