Dictionopolis has a real GDP per capita of $5,000, which is growing at 10% per year. Sitara has a real GDP per capita of $10,000, which is growing at 5% per year. Real GDP per capita for the two nations will converge in about years.

14 years

Explanation:

if we follow the rule of 70, their GDP's per capita will increase as follows:

                                            Dictionopolis                    Sitara

current GDP per capita           $5,000                        $10,000

in 7 years                                 $10,000

in 14 years                                $20,000                      $20,000

the rule of 70 is a simple way to determine how long will it take a certain amount of money to double given a compound interest rate.

Dictionopolis's GDP per capita will double every 70/10 = 7 years

Sitara's GDP per capita will double every 70/5 = 14 years

borrow money from the government then pay the government back 5k