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8 April, 05:51

You plan to work for Strickland Corporation for 12 years after graduation and after that want to start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandmother just gave you a $25,000 graduation gift that you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

a. $238,176

b. $250,712

c. $263,907

d. $277,797

e. $291,687

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Answers (2)
  1. 8 April, 08:30
    0
    D: $277,797

    Explanation:

    So I have made plans to work for strickland cooperation for 12 years after my graduation.

    Saving and depositing $7500 (t=1 to t=6)

    &

    $15,000 (t=7 to t=12)

    And a year before t = 1, I go a $25,000 gift from Grandma! Yay!

    So in my t=0, already have a head start of $25,000 with a compound interest of %9 every year on my saved capital.

    Year 1: $25,000 + (9/100) % of $25,000

    =$27,250 (this is my balance at the time of my first $7,500 deposit)

    Therefore after my deposit I have $34,750

    Year 2: $34,750 + (9/100) % of $34,750

    = $37,877.5 + $7,500

    = $45,377.5

    Year 3: $45,377.5 + (9/100) % of $45,377.5

    =$49,461.475 + $7500

    = $56,961.475

    Year 4: $56,961.475 + (9/100) % of $56,961.475

    = $62,028.00775 + $7,500

    = $69,588.00775

    Year 5: $69,588.00775 + (9/100) % of $69,588.00775

    =$75,850.92845 + $7,500

    = $83,350.92845

    Year 6: $83,350.92845 + (9/100) % of $83,350.92845

    = $90,852.51201 + $7,500

    = $98,352.51201

    Year 7: $98,352.51201 + (9/100) % of $98,352.51201

    = $107,204.2381 + $15,000

    = $122,204.2381

    Year 8: $122,204.2381 + (9/100) % of $122,204.2381

    = $133,202.6195 + $15,000

    = $148,202.6195

    Year 9: $148,202.6195 + (9/100) % of $148,202.6195

    = $161,540.8553 + $15,000

    = $174,540.8553

    Year 10: $174,540.8553 + (9/100) % of $174,540.8553

    = $192,429.5323 + $15,000

    = $207,429.5323

    Year 11: $207,429.5323 + (9/100) % of $207,429.5323

    = $226,098.1902 + $15,000

    = $241,098.1902

    Year 12: $241,098.1902 + (9/100) % of $241,098.1902

    = $262,797.0273 + $15,000

    = $277,797.0273

    (This will be my balance at the end of the twelfth year approximately $277,797)
  2. 8 April, 08:52
    0
    d. $277,797

    Explanation:

    Savings = $7,500 for the first 6 years (t = 1 through t = 6)

    Deposits = $15,000 for the following 6 years (t = 7 through t = 12)

    Gifts = $25,000

    Earnings = 9% annually

    Calculation of the Final Amount by Savings, Deposits and Gifts:

    Amount at the end of year 6

    Interest rate 9.0%

    1st Annuity (Savings) $7,500 $56,425 - Compounded at 9% 2nd Anuuity (Deposits) $15,000 NA

    Gift $25,000 NA

    Total Years 12

    Annuity years 6

    Amount at the end of year 12

    $94,630

    $112,850

    $70,317

    Final Amount: $277,797

    Therefore, $277,797 is the final amount which you will have when you start your business 12 years from now.
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