Question

Problem 9-46 Annuity consideration [LO9-4]

Your younger sister, Linda, will start college in five years. She has just informed your parents that she wants to go to Hampton University, which will cost $49,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda’s ambitions, your parents started investing $6,900 per year five years ago and will continue to do so for five more years. Use 11 percent as the appropriate interest rate throughout this problem (for discounting or compounding).

How much will your parents have to save each year for the next five years in addition to the $6,900 they are currently saving to have the necessary funds for Linda's education? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

Answer 1

	Uniform Series Present Worth factor:
	(P/A,i,N)=PWF=(((1+i)^N)-1)/(i((1+i)^N))
	i=Interest rate=11%=0.11
	N=number of years=4
	PWF=((1.11^4)-1)/(0.11*(1.11^4))=	3.10244569
	Amount Required after 15 years=PWF*49000	$        152,019.84
	Current savings per year=$6900
	Number of years of savings=5+5=10
	Compount Amount Factor(CAF)
	(F/A,i,N)=(((1+i)^N)-1)/i
	i=Interest rate=11%=0.11
	N=Number of years=10
	CAF=((1.11^10)-1)/0.11=	16.7220
	Future value of annual savings of $6900	$        115,381.86	(CAF*6900)
	Additional amount required	$          36,637.98	(152019.84-115381.86)
	Sinking fund factor
	(A/F,i,N)=SFF=i/(((1+i)^N)-1)
	i=Interest rate=11%=0.11
	N=number of years=5
	SFF=0.11/((1.11^5)-1)	0.16057031
	Additional annual amount of savings required	$             5,882.97	(0.16057031*36637.98)