Question

1. At an annual growth rate of 1.75% it will take _______  years for a country's GDP to double. If GDP starts at a value of $100 million, then in 200 years we would expect the value of GDP to be _______  times larger. 

2. If nominal GDP is growing at 5% per year, the inflation rate is 2% per year, and population growth is-190 per year then real GDP per capita is growing at _______ percent per year. 

3. A country aims to double real GDP per capita in the next 25 years. This means that on average real GDP per capita must grow at _______  per year. 

4. A country aims to double real GDP per capita in the next 25 years. If the rate of population growth in the country is 1% per year then this means that real GDP must grow at _______  per year. 4.

Answer 1

Let the initial GDP be x

Rate of growth = 1.75%

So, time taken so that he GDP is doubled=

Let the time taken in years be n. So,

2x = x(1.0175)ⁿ

2=(1.0175)ⁿ

n= 39.954 years.

If the current GDP is $100 million , then after 200 years , it will be = 100(1.0175)²⁰⁰= $3212.8 million.

Question 2) Nominal GDP = 5%, Inflation rate = 2% , Population Growth = -1%

Real gdp per capita = 5-2-(-1) = 4%

So real gdp per capita is growing at 4% per annum.

Question 3) Let the initial real GDP be x

Time = 25 years

In order to double the real GDP , rate of interest required=

Let the interest rate be i.

So, the equation will be =

2x = x(1+i)²⁵

2= (1+i)²⁵

i = 0.02811 = 2.811% per year.

Question 4) Let the initial real GDP be x

So the rate required for the real GDP to become 2x in 25 years when the population growth is 1% =

Let the interest rate be r

So the equation will be

2x = x(1+(r-(1/100)))²⁵

= 2= (1+(r-0.01))²⁵

= 1.02811 = 1+(r-0.01)

r = 0.03811 = 3.811%.