The government of a remote country collects $500B/year in taxes?

Government officials steal $600B/year.

The deficit is refinaced at rate 10%/year.

The banks are willing to lend the money as long as tax revenues remain sufficient to at least repay the interest.

After how many years will the govermnet declare bancruptcy?

The government of a remote country collects $500B/year in taxes?mortgage lenders

I think it%26#039;s about 17 years (could be 18 depending on how you treat the boundary conditions)

Of course, I am assuming definition of bankruptcy is when interest payment is more than $500b/year.

JohnVs Answer does not take into consideration that every year, the deficit you accumulate is $100b + the interest payment for that year. So, default happens quicker than the 19 years he suggested.

The government of a remote country collects $500B/year in taxes?

loan

An additional deficit of $100B is generated each year. At 10% p.a. this accumulates to -100*[(1.1)^n -1]/.1, or -1000 *(1.1^n) + 1000. Once this reaches $-5000B bankrupcy occurs: -5000 = -1000*(1.1^n) + 1000, or

-6 = -1(1.1^n) or 1.1^n = 6, and n ln(1.10, so n =ln(6)/ln(1.1) = 18.8. Gov%26#039;t will declare bankruptcy in year 19.