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2 March, 17:28

Today is your 20th birthday, and your parents just gave you $5,000 that you plan to use to open a stock brokerage account. You plan to add $500 to the account each year on your birthday. Your first $500 contribution will come one year from now on your 21st birthday. Your 45th and final $500 contribution will occur on your 65th birthday. You plan to withdraw $5,000 from the account five years from now on your 25th birthday to take a trip to Europe. You also anticipate that you will need to withdraw $10,000 from the account 10 years from now on your 30th birthday to take a trip to Asia. You expect that the account will have an average annual return of 12%. How much money do you anticipate that you will have in the account on your 65th birthday, following your final contribution

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  1. 2 March, 17:46
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    You anticipate that you will have $432,522 in the account on your 65th birthday, following your final contribution.

    Explanation:

    To calculate this, we use the formula for calculating the future value (FV) and FV of ordinary annuity as appropriate as given below:

    FVd = D * (1 + r) ^n ... (1)

    FVo = P * {[ (1 + r) ^n - 1] : r} ... (2)

    Where,

    FVd = Future value of initial deposit or balance amount as the case may be = ?

    FVo = FV of ordinary annuity starting from a particular year = ?

    D = Initial deposit = $5,000

    P = Annual deposit = s $500

    r = Average annual return = 12%, or 0.12

    n = number years = to be determined as necessary

    a) FV in five years from now

    n = 5 for FVd

    n = 4 for FVo

    Substituting the values into equations (1) and (2), we have:

    FVd = $5,000 * (1 + 0.12) ^5 = $8,812

    FVo = $500 * {[ (1 + 0.12) ^4 - 1] : 0.12} = $2,390

    FV5 = Total FV five years from now = $8,812 + $2,390 = $11,201

    FVB5 = Balance after $5,000 withdrawal in year 5 = $11,201 - $5,000 = $6,201.

    b) FV in 10 years from now

    n = 10 - 5 = 5 for both FVd and FVo

    Using equations (1) and (2), we have:

    FV of FVB5 = $6,201 * (1 + 0.12) ^5 = $10,928

    FVo = $500 * {[ (1 + 0.12) ^5 - 1] : 0.12} = $3,176

    FV10 = Total FV 10 years from now = $10,928 + $3,176 = $14,104

    FVB10 = Balance after $10,000 withdrawal in year 10 = $14,104 - $10,000 = $4,104

    c) FV in 45 years from now

    n = 45 - 10 = 35 for both FVd and FVo

    Using equations (1) and (2), we have:

    FV of FVB10 = $4,104 * (1 + 0.12) ^35 = $216,690

    FVo = $500 * {[ (1 + 0.12) ^35 - 1] : 0.12} = $215,832

    FV45 = Total FV 45 years from now = $216,690 + $215,832 = $432,522

    Conclusion

    Therefore, you anticipate that you will have $432,522 in the account on your 65th birthday, following your final contribution.
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