Your parents have accumulated a $170,000 nest egg. They have been planning to us
ID: 2733242 • Letter: Y
Question
Your parents have accumulated a $170,000 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 $26,000 to help her get started, and they have decided to take year-end vacations costing $12,000 per year for the next four years. Use 6 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 $26,660 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
a) Money available after Nail salon financing = $170,000 - $26,000 = $144,000
PVA = A × ({1 [1/(1+i )n ]} / i )
= $12,000 × ({1 [1/( 1.06 )4]} / .06 ) = $41,581.27
Current funds available for graduate school = Remaining balance after nail saloon financing PV of vacations
= $144,000 $41,581.27 = $102,418.70
b) Future value of graduate school funds in four years:
FV = PV × (1+ i )n = $102,418.70 × (1.06)4 = $129,301.30
Number of years of graduate school:
PVA = A × ({1 [1 / (1 + i )n]} / i )
(PV A / A ) × i ) 1 = [1 / (1 + i )n ]
=> (($129,301.30 / $26,660) × .06) 1 = (1 / 1.06 n )
.709 = (1 / 1.06n )
1.410439 = 1.06n
ln1.410439 = n × ln1.06
n = ln1.410439 / ln1.06
n = 5.90 years
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