Problem 129 - Beginning and Intermediate Algebra

Question

Solve each problem. In 2005, Americans saved \(-0.5 \%\) of their after-tax incomes. In September 2017 , they saved \(3.1 \%\). (Data from U.S. Bureau of Economic Analysis.) (a) Express the difference between these amounts as a positive number. (b) How could Americans have a negative personal savings rate in \(2005 ?\)

Step-by-Step Solution

Answer

Difference in savings rates: 3.6%. Negative savings in 2005 due to spending beyond income.

Step 1 - Understand the Given Data

Identify the savings rates for the given years: In 2005, the savings rate was \(-0.5 \%\) and in 2017, it was \(3.1 \%\).

Step 2 - Calculate the Difference in Savings Rates

Find the difference between the 2017 and 2005 savings rates:\( 3.1 - (-0.5) \)Simplify this to:\( 3.1 + 0.5 = 3.6 \% \)

Step 3 - Answer Part (a)

The difference between the savings rates in 2005 and September 2017 is \(3.6 \%\).

Step 4 - Explanation for Negative Savings Rate

A negative personal savings rate means that Americans were spending more than their after-tax income. This can happen if they are using savings, loans, or credit to finance their consumption.

Step 5 - Answer Part (b)

Americans had a negative personal savings rate in 2005 because they were spending more than their after-tax income, likely using savings or borrowing funds.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of a whole, where the whole is 100. Think of it as how much out of 100. For example, saying 20% is like saying 20 out of 100. In the context of personal savings rates, percentages tell us how much of the income people save out of what they earn. If you have a personal savings rate of 5%, it means you save 5 cents for every dollar you earn. To understand percentage changes, we often calculate the difference between two percentages. As shown in the exercise, going from -0.5% in 2005 to 3.1% in 2017, we get a difference of 3.6%. This means the savings rate improved by 3.6 percentage points between the two years.

Economic Analysis

Economic analysis involves looking at data to understand and predict economic behaviors. Analyzing personal savings rates helps to understand how much people save from their income over time. Different factors like income, expenses, and economic policies affect these rates. For instance, low savings rates might indicate that people are spending most of their income, whereas high savings rates suggest more money is being saved.

Economic analysts look at these rates to gauge financial health. If people save more, it could mean they feel secure. On the other hand, spending more than they earn might indicate economic distress or confidence in future income. For the exercise, the shift from a -0.5% to a 3.1% savings rate could hint at either improving financial situations or changing economic behaviors.

Negative Savings Rate

A negative savings rate is a situation where people spend more than they earn. It means they are either dipping into their savings or borrowing money to make up for the shortfall. This scenario can arising due to increased spending, reduced income, or both. For example, unexpected expenses like medical bills can result in negative savings rates.

The exercise mentions a -0.5% savings rate in 2005, meaning Americans spent slightly more than they earned. This could be due to various reasons, such as easy credit access, desire to maintain living standards, or economic uncertainty. A repeated negative savings rate can lead to higher debt, which can be risky for long-term financial health.

To sum up, understanding why and how negative savings rates occur helps individuals and policymakers make better financial decisions. This awareness can guide strategies to encourage savings and reduce excessive debt.