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Your parents have accumulated a $140,000 nest egg. They have been planning to us

ID: 2818374 • Letter: Y

Question

Your parents have accumulated a $140,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo college and start a nail salon. Your parents are giving Courtney $17,000 to help her get started, and they have decided to take year-end vacations costing $7,000 per year for the next four years. Use 7 percent as the appropriate interest rate throughout this problem. Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

   
a. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? (Round your final answer to 2 decimal places.)
Funds available for graduate school =

b. You plan to work on a master’s and perhaps a PhD. If graduate school costs $21,980 per year, approximately how long will you be able to stay in school based on these funds? (Round your final answer to 2 decimal places.)

Number of years =
  

0515 1122346803120 39 5 66 6 2 6 9 5 2 1 2 2 6 599 135 1112334579148 2 0 5297 8327 220872 1112223456780258 579 137 9741 1357914793 2 05 52 0 9 5 5 5 8 7 7 7 24 1245791368469 9749234 9472771 125191662 70 1. · 111122334567801469 23 27 62 43 50 27 09242511874 11112233445 50-1: 456778901245633 488 111-1. 2 2 2 3 3 4 55679024690580 877 1913 678152 2 11112223344567890246 01369 69385 9552 768 5 677 7647 5678913 0123467 95 247148 41866 1234567890123456789 123456789012345678905

Explanation / Answer

A. First we need to calculate the Present value of all the four vacation cost they are planning

PV of annuity=A*((1-(1/(1+r)^n))/r)

=7000*((1-(1/(1.07^4))/0.07)

=7000*((1-0.76)/0.07)

= 7000*3.387= $23710.48

Fund available for graduate school in Present day = Saving- Nail Saloon financing- Present value of vacations

= 140000-17000-23710.48= $99289.52.

Now we need to calculate the Future value of fund available after 4 year

FV= Fund available*(1+r)^n

= 99289.52*(1.07^4)= $130148.31

B PV of annuity=A*((1-(1/(1+r)^n))/r)

130148.31= 21980*((1-(1/(1.07)^n))/0.07)

(130148.31/21980*0.07)-1=-(1/1.07^n)

= -0.586=-(1/1.07^n)

= 1.07^n= 1/0.586

=1.07^n= 1.708

= n log 1.07=Log 1.708

= n= Log 1.708/ Log 1.07

= n= 7.91