Question

If real GDP grows at 7 percent per year, then real GDP will double in approximately _____ years. a. 70 b. 14 c. 10 d. 7

Short answer

c. 10

Step-by-step solution

Understanding the Problem

We need to find the number of years it takes for real GDP to double given an annual growth rate of 7%. This is a classic application of the 'Rule of 70'.

Introduction to the Rule of 70

The 'Rule of 70' is a way to estimate the number of years it takes for a quantity to double, given its annual growth rate. The formula is \(\text{years to double} = \frac{70}{\text{growth rate}}\).

Applying the Rule of 70

Given an annual growth rate of 7%, use the formula: \(\text{years to double} = \frac{70}{7}\).

Calculating the Number of Years

Calculate \(\frac{70}{7} = 10\). This means it will take approximately 10 years for the real GDP to double.

Identifying the Correct Option

From the given options, the calculation matches option c, which is 10 years.

Key concepts

Rule of 70

The Rule of 70 is a simple formula used to estimate the number of years required for a quantity to double given its annual growth rate. It's a handy rule of thumb used in economics and finance when dealing with exponential growth processes. The formula is expressed as:

• \( \text{years to double} = \frac{70}{\text{growth rate}} \)

This formula applies because exponential growth processes have a consistent growth rate. The number 70 is used because it's a good approximation for early approximations of natural logarithms, which are the theoretical basis for this rule.
When you know the annual growth rate, you can plug it into this formula to get an approximate number of years needed for the quantity to double. This is particularly useful in evaluating economic indicators like real GDP.

Real GDP

Real Gross Domestic Product, or Real GDP, measures a country's economic output, adjusted for inflation or deflation, over a certain time period. It's an essential indicator used in macroeconomics to assess the health of an economy.
Real GDP provides a more accurate reflection of an economy’s size and how it’s growing over time. By adjusting for inflation, it removes the distortions caused by rising prices, per the measure of nominal GDP.

• Reflects the total value of goods and services produced.
• Allows comparisons across different years without inflation effects skewing the results.

Tracking Real GDP helps economies and planners gauge economic efficiency and living standards, guide policy decisions, and forecast future economic conditions.

Annual Growth Rate

The annual growth rate signifies how much an economic variable like GDP increases each year. It is calculated to assess how quickly an economy or a company is growing on average annually.
This rate is typically expressed as a percentage and can apply to various economic metrics such as GDP, investments, or population growth.

• Monthly or quarterly data can be used to calculate annual rates.
• This metric helps in comparing growth performance across different economic sectors or countries.

When using it for longer-term economic planning, the annual growth rate allows analysts to predict future performances based on past trends.

Doubling Time

Doubling time is the period it takes for a quantity to double its size at a constant rate of growth. It is closely related to the Rule of 70 to estimate when a population or capital will double.

• Key for planning and projecting long-term growth.
• Applies across contexts including population growth, investments, and economic output.

It allows policymakers, businesses, and investors to assess how rapidly changes in elements like GDP or investments could progress under stable conditions. Understanding doubling time offers insights into the sustainability and potential implications of growth trends.