Your parents have accumulated a $130,000 nest egg. They have been planning to us
ID: 2784690 • Letter: Y
Question
Your parents have accumulated a $130,000 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 $16,000 to help her get started, and they have decided to take year-end vacations costing $8,000 per year for the next four years. Use 8 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 $21,460 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_____
Explanation / Answer
Solution A Year Cash flow Help for Salon Vacation Net Amount FV factor @ 8% Future value 0 130,000 (16,000) - 114,000 1.3605 155,096 1 (8,000) (8,000) 1.2597 (10,078) 2 (8,000) (8,000) 1.1664 (9,331) 3 (8,000) (8,000) 1.0800 (8,640) 4 (8,000) (8,000) 1.0000 (8,000) Net Future value 119,047 So Parents will have 119,047 at the end of 4 years Solution B Annual Withdrawl 21460 So the PV of all such withdrawls should be equal to 119,047 PV of annuity for making pthly payment P = PMT x (((1-(1 + r) ^- n)) / i) Where: P = the present value of an annuity stream PMT = the dollar amount of each annuity payment r = the effective interest rate (also known as the discount rate) i=nominal Interest rate n = the number of periods in which payments will be made 119,047 =21460*(((1-(1 +8%) ^-n)) /8%) 119047/21460 =(((1-(1 +8%) ^-n)) /8%) 5.547 =(((1-(1 +8%) ^-n)) /8%) =5.547*8% =((1-(1 +8%) ^-n)) 0.444 =((1-(1 +8%) ^-n)) =0.44376-1 =-(1 +8%) ^-n (0.556) =-(1 +8%) ^-n 0.556 =(1 +8%) ^-n Log 0.556 =-nlog1.08 -0.2549 =-n*0.0334 =0.2549/0.0334 =n n= 7.63 So he can survive in college for next 7.6 years
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