Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

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)