Question

In which of the following cases was the inflation rate 12 percent over the last year?
a.

One year ago the price index had a value of 110 and now it has a value of 120.
b.

One year ago the price index had a value of 145 and now it has a value of 163.
c.

One year ago the price index had a value of 134 and now it has a value of 150.
d.

One year ago the price index had a value of 120 and now it has a value of 132.

Answer 1

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.