In 2015, India's Gross Domestic Product (GDP) at current prices was $₹151$ trillion and the population was $1.31$ billion. By 2020, GDP rose to $₹210$ trillion and population to $1.38$ billion. Assuming inflation of 5 % per year, calculate the average annual growth rate of real per‑capita GDP over this period. Express your answer in percent, rounded to two decimal places.

Step-by-step solution

1. Compute nominal per‑capita GDP for 2015: $\frac{151\times 10^{12}}{1.31\times 10^9}=115,267.94$ rupees.
2. Compute nominal per‑capita GDP for 2020: $\frac{210\times 10^{12}}{1.38\times 10^9}=152,173.91$ rupees.
3. Calculate the price deflator for 5 years of 5 % inflation: $(1+0.05{)}^5=1.27628$.
4. Convert nominal figures to real (2015 constant) terms:
5. Real per‑capita 2015 = $\frac{115,267.94}{1.27628}=90,361.00$ rupees.
6. Real per‑capita 2020 = $\frac{152,173.91}{1.27628}=119,210.00$ rupees.
7. Find the total growth factor over 5 years: $\frac{119,210}{90,361}=1.319$.
8. Derive the average annual growth rate: $(1.319{)}^{1/5}-1$.
9. Take natural log: $\ln (1.319)=0.277$, divide by 5: $0.0554$, exponentiate: $e^{0.0554}=1.0570$.
10. Subtract 1 and convert to percent: $1.0570-1=0.0570=5.70\%$.
11. Therefore, the average annual real per‑capita GDP growth rate is 5.70 %.

Concept tested: Real per‑capita GDP growth

Published 30 August 2026 · How this solution was prepared and checked

Related questions

• 1 Discuss two development strategies that the Indian government has adopted to promote inclusive growth. Explain how each strategy helps reduce poverty and inequality.
• 2 Suppose a small village consists of only four families. The monthly incomes of three of these families are ₹ 7,000, ₹ 8,000, and ₹ 10,000. If the average per capita monthly income of the village is ₹ 9,000, calculate the monthly income of the fourth family.
• 3 Ramu is a 20-year-old worker who weighs 40 kg and has a height of 1.60 m. Calculate his Body Mass Index (BMI) using the formula BMI = (Weight in kg)/(Height in m)^2, and state whether he is undernourished, normal, or overweight.
• 4 Groundwater is a renewable resource, yet many regions in India face severe groundwater depletion. Explain three major reasons for this depletion and suggest two measures to achieve sustainable groundwater management.
• 5 Why is per capita income alone not a sufficient indicator of human development? State two reasons.
• 6 Suppose the Lorenz curve for a country is approximated by the points (0,0), (0.25,0.10), (0.5,0.30), (0.75,0.55), (1,1). Using the trapezoidal rule, the Gini coefficient can be calculated as G = 1 - 2 × (area under Lorenz curve). Which of the following is the correct Gini coefficient?