Answer
$10.24$ years
Work Step by Step
We have:
Leader GDP per capita: $\$40,000$
Follower GDP per capita: $\$20,000$
Leader growth rate: $0\%$
Follower growth rate: $7\%$
We use the formula:
$\text{Years}=\frac{\ln\frac{40,000}{20,000}}{\ln(1+0.07)}\approx 10.24$
So there are $10.24$ years to catch up.
