SOLUTION: Gilberto opened a savings account for his daughter and deposited $1500 on the day she was born. Each year on her birthday, he deposited another $1500. If the account pays 9% intere

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Question 890679: Gilberto opened a savings account for his daughter and deposited $1500 on the day she was born. Each year on her birthday, he deposited another $1500. If the account pays 9% interest, compounded annually, how much is in the account at the end of the day on her 11th birthday?
Answer by Lapric(19) About Me  (Show Source):
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Gilberto opened a savings account for his daughter and deposited $1500 on the day she was born. Each year on her birthday, he deposited another $1500. If the account pays 9% interest, compounded annually, how much is in the account at the end of the day on her 11th birthday?
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For this question you can use the compound interest formula +A%28t%29=+P%281%2B%28r%2Fn%29+%29%5Ent+
Where r= 0.09 (interest rate per year), n= 1 (number of times interest is compounded per year),P= Principal(the amount put in the account) t= 1 (number of years), and A(t) is amount after t years.
So now our formula is +A%28t%29+=+%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+
When Gilberto's daughter is born he puts in 1,500.
When she is 1 year old the account amount is A(t) = 1,500(1+(0.09/1))^((1)(1)) which equals $1,635 since it's her birthday, he deposits another 1,500 dollars. So now the amount in her account is 1635+1500= $3,135
When she is 2 years old, A(t) = 3,135(1+(0.09/1) )^((1)(1)) = 3,417.15. 3,417.15+1,500 = $4,917.15
When she is 3 years old, A(t) = 4,917.15(1+(0.09/1) )^((1)(1)) =5,359.69. 5,359.69+1,500= $6,859.69
When she is 4 years old, A(t) = 6,859.69(1+(0.09/1) )^((1)(1)) =7,477.07. 7,477.07+1,500= $8,977.07
When she is 5 years old, A(t) = 8,977.07(1+(0.09/1) )^((1)(1)) =9,785. 9,785+1,500= $11,285
When she is 6 years old, A(t) = 11,285(1+(0.09/1) )^((1)(1)) =12,300.65. 12,300.65+1,500= $13,800.65
When she is 7 years old, +A%28t%29+=+13800.65%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+ =15,042.71. 15,042.71+1,500= $16,542.71
When she is 8 years old, +A%28t%29+=+16542.71%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+ =18,031.55. 18,031.55+1,500= $19,531.55
When she is 9 years old, +A%28t%29+=+16542.71%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+ =21,289.39. 21,289.39+1,500= $22,789.39
When she is 10 years old, +A%28t%29+=+22789.39%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+ =24,840.44. 24,840.44+1,500= $26,340.44
When she is 11 years old, +A%28t%29+=+26340.44%281%2B%280.09%2F1%29+%29%5E%28%281%29%281%29%29+ =28,711.08. 28,711.08+1,500= $30,211.08
So after 11 years, Gilberto's daughter has $30,211.08 in her account and this girl is going to have a pretty awesome college account lol. Hope this helps you.