Question

An economy starts off with a per capita GDP of 20,000 euros. How large will the per capita GDP be if it grows at an annual rate of 4% for 10 years?

Answer 1

The GDP per capita of an economy starting at 20,000 euros and growing at an annual rate of 4% for 10 years would be 29,604.80 euros.

Step-by-step explanation:

To determine the future GDP per capita given an initial GDP per capita, a growth rate, and a number of years, we use the formula for compound interest:

FV = PV × (1 + r)^n

Where:

• FV is the future value (future GDP per capita).
• PV is the present value (initial GDP per capita).
• r is the annual growth rate (expressed as a decimal).
• n is the number of years.

In this case:

• PV = 20,000 euros
• r = 4% or 0.04
• n = 10 years

Using the formula, we calculate the future GDP per capita:

FV = 20,000 × (1 + 0.04)^10

This equals:

FV = 20,000 × (1.04)^10

FV = 20,000 × 1.48024

FV = 29,604.80 euros

So after 10 years, at an annual growth rate of 4%, the GDP per capita would be 29,604.80 euros.