question archive When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account bearing a 5% compounded annual rate on each birthday, beginning with your first
When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account bearing a 5% compounded annual rate on each birthday, beginning with your first
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When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account bearing a 5% compounded annual rate on each birthday, beginning with your first. You have just turned 22 and want the dough. However, it turns out that dear old (forgetful) Aunt Minnie made no deposits on your fifth and eleventh birthdays. How much is in the account right now?
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Answer:
Annual Deposit = $1,000
Number of Deposits = 20
Interest Rate = 5%
Deposits were not made on 5th and 11th birthday
Accumulated Sum = $1,000*1.05^21 + $1,000*1.05^20 + … + $1,000*1.05 + $1,000 - $1,000*1.05^17 - $1,000*1.05^11
Accumulated Sum = $1,000 * (1.05^22 - 1) / 0.05 - $1,000 * 1.05^17 - $1,000 * 1.05^11
Accumulated Sum = $1,000 * 38.50521 - $1,000 * 2.29202 - $1,000 * 1.71034
Accumulated Sum = $34,502.85
