In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000 is taxed at 15%. How much tax is assessed on $13,000?

First, we determine how much income is over $10,000 but not over $20,000 by subtracting $10,000 from $13,000 to find $3,000.

Next, we multiply this income by the 10% tax rate to find the tax assessed so far, which is $3,000 * 0.10 = $<<3000*0.10=300>>300.
Then we subtract the $3,000 income from the $13,000 income to find the remaining income, $13,000 - $3,000 = $<<13000-3000=10000>>10,000.
Next, we find the tax assessed on this remaining income by multiplying it by the 10% tax rate, $10,000 * 0.10 = $<<10000*0.10=1000>>1,000.
Finally, we add these two taxes to find the total tax assessed, $1,000 + $300 = $<<1000+300=1300>>1,300. Answer: \boxed{1300}.

To determine the amount of tax assessed on $13,000, we need to calculate the tax amount for each applicable tax bracket.

1. The first tax bracket is for income up to $10,000, which is not taxed. So, there is no tax assessed on the first $10,000 of income.

2. The remaining $3,000 ($13,000 - $10,000) falls within the second tax bracket, where any income over $10,000 but not more than $20,000 is taxed at a rate of 10%.

To calculate the tax for this bracket, we multiply the income in this bracket by the tax rate of 10%:

Tax in the second bracket = ($3,000) * (10%)
= $300.

Therefore, the tax assessed on $13,000 is $300.