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8 September, 10:02

The parents of a young child decide to make annual deposits into a college savings account. The first deposit will be made on her 5th birthday and the last deposit will be made on her 15th birthday. Then starting on her 18th birthday, withdrawals for college expenses will be made as follows: $20,000 on her 18th birthday, $24,000 on her 19th birthday, $28,000 on her 20th birthday, and $32,000 on her 21st birthday. If the yearly interest rate is 10%, during this entire period of time, what is the amount of the equal, annual deposits made on birthdays 5 through 15

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  1. 8 September, 10:28
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    The amount of the equal, annual deposits made on birthdays 5 through 15 is $3,970.58

    Explanation:

    First, let's calculate the present value of the college expenses on her 17th birthday (a year before college) using NPV formula

    NPV (9%, 20000 ... 32000) = $82,839.69

    Now, its value on 15th birthday should be equal to 82,839.69 / (1 + 9%) ² = $69,724.51

    Using the PMT formula, we can calculate the annual amount they have to invest for 11 years to get to this sum at 9% annual rate

    PMT (rate = 9%, nper = 11, pv = 0, fv = 69,724.51, 0) = $3,970.58
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