Question 1

The formula for the rule of 70,where n is number of years and r is growth rate,is expressed as:

Accepted Answer

The correct formula for the rule of 70, which is used to estimate the number of years it will take for an investment or population to double at a given annual growth rate, is expressed as $ n = \frac{70}{r} $. However, none of the provided options exactly match this formula. The closest option, when rearranged, is D) $ n * r = 70 $, which can be rewritten to resemble the correct formula by dividing both sides by $ r $, thus giving $ n = \frac{70}{r} $.

Question 2

If real GDP grows at an annual rate of 1%,it will double in approximately _____ years.

Accepted Answer

The rule of 70 states that to find the approximate number of years for a variable to double, divide the number 70 by the annual growth rate. Therefore, 70/1=70, which means it will take approximately 70 years for real GDP to double with an annual growth rate of 1%. Choice (D) is the correct answer.

Question 3

Suppose that real GDP per capita of Canada is $32 000 and its growth rate is 2% per year and that real GDP per capita of China is $4 000,and its annual growth rate is 7%.How many years will it take for China's real GDP per capita to be larger than real GDP per capita in Canada?

Accepted Answer

Using the formula for calculating the future value of an asset with continuous compounding:

FV = PV e^(r * t)

where: 
FV = future value 
PV = present value 
r = annual growth rate 
t = time period

We can set up the inequality:

$4,000 e^(0.07t) > $32,000 e^(0.02t)

Simplifying:

e^(0.05t) > 8

Taking the natural log of both sides:

0.05t > ln(8)

t > ln(8)/0.05 ≈ 35.5

Therefore, it will take about 40-45 years for China's real GDP per capita to be larger than real GDP per capita in Canada.

Question 4

India is growing at a rate of 9% per year,and its real GDP per capita is about $3 500,while Canada is growing at a rate of 3% per year,and its real GDP per capita is about $47 000.How long will it take India to double its real GDP per capita?

Accepted Answer

To find the time it takes for India's GDP per capita to double, we use the Rule of 70, which states that the doubling time is approximately 70 divided by the growth rate. For India, this is 70 / 9 = 7.8 years.

Question 5

There are two countries on a peninsula.The first has a per capita annual growth rate of 2%,and its neighbour to the south has an annual growth rate of 5%.How much sooner will the country in the south double its GDP per capita than will its neighbour in the north?

Accepted Answer

The Rule of 70 estimates doubling time by dividing 70 by the growth rate. For the south, it's 70/5 = 14 years. For the north, it's 70/2 = 35 years. The difference is 35 - 14 = 21 years.

Question 6

Suppose that real GDP per capita of Canada is $32 000 and its growth rate is 2% per year and that real GDP per capita of China is $4 000,and its annual growth rate is 7%.According to the rule of 70,how large will China's real GDP per capita be in 20 years?

Accepted Answer

According to the rule of 70, we can find the number of years it takes for a variable to double by dividing 70 by its annual growth rate.

For Canada: 
70/2 = 35 years to double

After 20 years, Canada's real GDP per capita would be: 
$32 000 x (1 + 0.02)^20 = $44 962.29

For China: 
70/7 = 10 years to double

After 20 years, China's real GDP per capita would be: 
$4 000 x (1 + 0.07)^20 = $16 041.64

Therefore, the best choice is C) $16 000.

Question 7

India is growing at a rate of 9% per year,and its real GDP per capita is about $3 500,while Canada is growing at a rate of 3% per year,and its real GDP per capita is about $47 000.About how much will India's real GDP per capita be in 20 years?

Accepted Answer

India's real GDP per capita will be approximately $20,000 in 20 years. This is because India's real GDP per capita is growing at a rate of 9% per year, which means that it will double every 8 years. In 20 years, India's real GDP per capita will have doubled twice, which means that it will be 4 times its current value. $3,500 x 4 = $20,000.

Question 8

Suppose that real GDP per capita of Canada is $32 000 and its growth rate is 2% per year and that real GDP per capita of China is $4 000,and its annual growth rate is 7%.How long will it take real GDP per capita of Canada to double?

Accepted Answer

The rule of 70 is used to estimate the doubling time of an investment or economy. It states that you divide 70 by the annual growth rate to find the doubling time. For Canada, with a growth rate of 2%, it will take 70 / 2 = 35 years for the real GDP per capita to double.

Question 9

India is growing at a rate of 9% per year,and its real GDP per capita is about $3 500,while Canada is growing at a rate of 3% per year,and its real GDP per capita is about $47 000.How long will it take Canada to double its real GDP per capita?

Accepted Answer

To calculate the number of years it takes for Canada to double its real GDP per capita, we can use the rule of 70. The rule of 70 states that to find the approximate number of years for a variable to double, you can divide 70 by the annual growth rate of that variable.

For Canada, the annual growth rate is 3%, so dividing 70 by 3 gives us approximately 23.3. Therefore, it will take Canada about 23.3 years to double its real GDP per capita.

Question 10

India is growing at a rate of 9% per year,and its real GDP per capita is about $3 500,while Canada is growing at a rate of 3% per year,and its real GDP per capita is about $47 000.About how much will Canadian real GDP per capita be in 14 years?

Accepted Answer

To find the future GDP per capita, use the formula: Future GDP = Present GDP * (1 + growth rate)^number of years. For Canada: $47,000 * (1 + 0.03)^14 ≈ $71,000.

Question 11

Suppose that real GDP per capita of Canada is $32 000 and its growth rate is 2% per year and that real GDP per capita of China is $4 000,and its annual growth rate is 7%.How long will it take China's real GDP per capita to double?

Accepted Answer

To double its real GDP per capita, China needs its GDP per capita to increase by 100%.
Using the formula for the Rule of 70, which states that the number of years it takes for a variable to double is approximately 70 divided by the annual growth rate of the variable, we can calculate: 
For Canada: 
70/2 = 35 years
For China: 
70/7 = 10 years.

Question 12

If real GDP doubles in 35 years,its average annual growth rate is approximately:

Accepted Answer

The average annual growth rate can be approximated using the Rule of 70, which states that the number of years it takes for a variable to double is approximately 70 divided by the annual growth rate. Given that it takes 35 years for real GDP to double, dividing 70 by 35 gives an annual growth rate of approximately 2%.

Question 13

If real GDP per capita grows at 5% per year consistently over time,how many years will it take for it to double?

Accepted Answer

The rule of 70 states that if a variable grows at a constant rate of x% per year, it will double in approximately 70/x years. Using this rule, we find that real GDP per capita will double in approximately 70/5 = 14 years. Therefore, the best choice is C) 14.

Question 14

According to the rule of 70,if a country doubles its real GDP per capita every 20 years,that country must be growing at an annual rate of:

Accepted Answer

The rule of 70 states that to find the approximate number of years for a variable to double, we divide 70 by the annual growth rate. 
Therefore, in this case,

70 / Annual Growth Rate = 20

Annual Growth Rate = 70 / 20 = 3.5%

So the correct answer is B, which is 3.5%.

Question 15

The rule of 70 states that:

Accepted Answer

The rule of 70 states that the number of years for a variable to double equals 70 divided by its annual growth rate. This is a commonly used rule of thumb in finance, economics, and other fields that deal with exponential growth or decay.

Question 16

If real GDP grows at an average rate of 3% per year,it will double in _____ years.

Accepted Answer

The rule of 72 states that if you divide the annual growth rate into 72, you get the approximate number of years it takes for the variable to double. Therefore, if real GDP grows at an average rate of 3% per year, it will double in approximately 23 years (72/3=24). So the best choice is C.

Question 17

Real GDP per capita,growing at a constant rate over a 35-year period,has doubled at the end of that period.What must the annual growth rate of real GDP per capita be for this economy?

Accepted Answer

The annual growth rate required for real GDP per capita to double over a 35-year period can be found using the Rule of 70, which states that the doubling time of an investment can be found by dividing 70 by the annual growth rate. Rearranging this formula to solve for the growth rate gives us the growth rate = 70 / doubling time. Substituting 35 years for the doubling time, we get a growth rate of approximately 2% per year.

Question 18

If output is growing at 5% annually,how many years will it take for output to quadruple?

Accepted Answer

The answer of If output is growing at 5% annually,how...

Question 19

The rule of 70 is MOST useful in:

Accepted Answer

The rule of 70 helps to estimate the doubling time of real GDP for a given growth rate, which is particularly useful in understanding economic growth trends and projections. It is not useful in identifying the causes or sources of economic growth, nor does it provide information on the productivity of labour.

Question 20

If real GDP doubles in 12 years,its average annual growth rate is approximately:

Accepted Answer

The answer of If real GDP doubles in 12 years,its...

Quiz 9: Long-Run Economic Growth