The smiths spent $2,000 on clothes in a particular year. if they increase the amount they spend on clothes by 10% each year, the smiths will spend a total of $ clothing in 4 years

In 1 year:$2200
In 2 years:$2420
In 3 years:$2662
In 4 years:$2928.20

Then, find the sum, which in this case is $10,210.20

What is 10% of 2,000 ? 200. 
so 2,000+200 = 2,200 for the 1st year

What is 10% of 2,200 ? 220. 
2,200+220 = 2420 for the 2nd year

What is 10% of 2,420 ? 242. 
2420 + 242 = 2662 for the 3rd year

What is 10% of 2662 ? 266.2 
2662 + 266.2 = 2928.2 

So that's how much they spent each year, now to get the total we add them together. 
2928.2 + 2,662. + 2,420. + 2,200. = 10,210.2