Question

You want to buy a condo 5 years from now, and you plan to save $3,000 per year, beginning one year from today. you will deposit the money in an account that pays 6% interest. how much will you have just after you make the 5th deposit, 5 years from now?

Answer 1

Beginning with the last deposit and working toward the present, the amount in the account is
  3000 + 3000*1.06 + 3000*1.06^2 + 3000*1.06^3 + 3000*1.06^4
  = 3000*(1.06^5 -1)/(1.06 -1)
  = 16,911.28 . . . dollars

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The sum is found using the formula for the sum of a geometric series. For first term a1 and common ratio r, that sum is
  Sn = a1*(r^n -1)/(r -1)
Your series has a1=3000 and r = 1.06. It has 5 terms (n=5).