Question

If you put $10 in a savings account at the beginning of each month for 15 years, how much money will be in the account at the end of the 10th year? assume that the account earns 12% compounded monthly and round to the nearest $1. $5,046

Answer 1

After 10 years, there will have been 120 deposits. The last one earns 12%/12 = 1% interest, so is mutipied by 1.01. The one before is multiplied by 1.01². Overall, you have the sum of a geometric series of 120 terms with first term 10.10 and common ratio 1.01. That sum is given by the general formula
  Sn = a1·(r^n -1)/(r -1)
  S120 = 10.10(1.01^120 -1)/(1.01 -1)
  S120 = 1010·2.30038689 ≈ 2323

At the end of the 10th year (before the first deposit of the 11th year), the account balance will be
  $2,323