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Butoxors [25]
3 years ago
15

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 en

d of the 10th year? assume that the account earns 12% compounded monthly and round to the nearest $1. $5,046
Mathematics
1 answer:
Vika [28.1K]3 years ago
6 0
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
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