Question

Your parents have accumulated a $160,000 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 $31,000 to help her get started, and they have decided to take year-end vacations costing $11,000 per year for the next four years. Use 9 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 $29,260 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.)

Answer 1

Solution a
	Funds available	$         160,000
	Funds given to Courtney for salon	$           31,000
	Remaining funds	$         129,000
	Amount after 4 years @ 6%	129000*(1+9%)^4
	Amount after 4 years @ 6%	$    182,094.03
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / r)
	Where:
	P = the future value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$           11,000
	r = the effective interest rate (also known as the discount rate)	9.00%
	n = the number of periods in which payments will be made	4
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
	FV of annuity=	11000* ((((1 + 9%) ^ 4) - 1) / 9%)
	FV of annuity=	$      50,304.42
	So funds available for graduation=	182094.03-50304.42
	So funds available for graduation=	$    131,789.61
Solution b
	PV of college education fee
	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream	$    131,789.61
	PMT = the dollar amount of each annuity payment	$           29,260
	r = the effective interest rate (also known as the discount rate)	9.00%
	n = the number of periods in which payments will be made	To be computed
	PV of annuity=	PMT x (((1-(1 + r) ^- n)) / r)
	131789.61=	29260* (((1-(1 + 9%) ^- n)) / 9%)
	(131789.61/29260)*9%=	1-(1.09) ^- n
	0.405367900960356=	1-(1.09) ^- n
	1-0.405367900960356=	1.09^- n
	0.594632099039644=	1.09^- n
	Log 0.594632099039644=	-n*Log 1.09
	(0.23)	-n*0.0374264979406237
	N=	0.22575165069865/0.0374264979406237
	N=	6.03	Years