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Your parents have accumulated a $150,000 nest egg. They have been planning to use this money...

Your parents have accumulated a $150,000 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 $18,000 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.)

b. You plan to work on a master’s and perhaps a PhD. If graduate school costs $22,500 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.)

Solutions

Expert Solution

a. Your parents have accumulated a $150,000 nest egg

Amount given to your sister Courtney at beginning of year 1 = $18,000

Therefore Remaining Balance = $150,000 - $18,000 = $132,000

Year (t)

Fund at the beginning of year (A)

Interest earned at 6% (I) (I= A *6%)

Amount withdrawn for year-end vacations (B)

Remaining Balance at end of year (A+I-B)

1

$132,000.00

$7,920.00

$12,000

$127,920.00

2

$127,920.00

$7,675.20

$12,000

$123,595.20

3

$123,595.20

$7,415.71

$12,000

$119,010.91

4

$119,010.91

$7,140.65

$12,000

$114,151.57

Your parents will have $114,151.57 at the end of four years to help you with graduate school.

b. Now we can use following Present Value of an Annuity formula to calculate the period of annual withdrawals of $22,500 with 6% interest rate

PV of fund = PMT * [1-(1+i) ^-n)]/i

Where

Present value of fund at the end of year 4 (PV) = $114,151.57

Annual withdrawals PMT =$22,500

Number of annual withdrawals n =?

Annual interest rate I =6%

Therefore

$114,151.57 = $22,500 * [1- (1+6%) ^-n]/6%

Or n = 6.23 years

Therefore you be able to stay in school for 6.23 years based on these funds.

jeff jeffy answered 2 years ago
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