India’s per capita income was 2,500 in 2020. Pakistan’s per capita income was 2,000 in 2020. (a) Compute the CAGR of per capita income for each country over 30 years. (b) If both countries grow at 4% per year for the next 10 years starting from 2020, what will be the per capita incomes in 2030? (c) Which country will have a higher per capita income in 2030 and why?
Answer
India: 3.87%, Pakistan: 1.72%; 2030: India ≈₹3,701, Pakistan ≈₹2,960; India higher because of higher base and past CAGR
The correct answer is India: 3.87%, Pakistan: 1.72%; 2030: India ≈₹3,701, Pakistan ≈₹2,960; India higher because of higher base and past CAGR — (c) 3700>2960 → India has higher 2030 per capita income; higher past CAGR and larger current base lead to larger compounding.
Step-by-step solution
- (a) India: Ratio 2500/800=3.125; ln=1.1398; /30=0.03799; exp=1.0387; CAGR=3.87%.
- Pakistan: Ratio 2000/1200=1.6667; ln=0.5108; /30=0.01703; exp=1.0172; CAGR=1.72%.
- (b) Compute (1+0.04)^10≈1.4802.
- India 2030: 2500×1.4802≈3700.5.
- Pakistan 2030: 2000×1.4802≈2960.4.
- (c) 3700>2960 → India has higher 2030 per capita income; higher past CAGR and larger current base lead to larger compounding.
Common mistake: Using simple growth or wrong base; ignoring compounding
Concept tested: CAGR, compound growth, comparative analysis
Published · How this solution was prepared and checked
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