Question

10. Your parents promise to buy your dream car upon graduation from college with your Masters Degree. Your dream car is expected to cost $60,000 in six years. If your parents earn an average return of 8% for 6 years, what amount must they invest each year in order to accumulate $60,000.

11. If upon graduation (age 21) you decide to invest in a 401K. You begin at age 21 and invest $3,000 per year for 10 years and then stop. If you wait until age 61 (another 30 yrs) to remove the funds, how much will the funds be worth assuming an average return of 10%? (hint; this requires 2 calculations)

Answer 1

1	Future Value (FV)	60000
	Rate of Return (r')	8%
	No of Years (n)	6
	PV=	(FV*r)/(((1+r)^n)-1)
	=	(60000*0.08)/(((1+0.08)^6)-1)
	=	8,178.92
	Parents must invest $8178.92 evey year to accumulate $60000 in 6 years
2	Yearly Payment (PMT)	3,000.00
	No of Years (n)	10.00
	Rate(r')	10%
	PV of value accumalted funds at the end of 10 years=	PMT*(1-((1+r)^-n))/r)
	=	3000*(1-((1+0.1)^-10))/0.1
	=	18,433.70
	FV value of $18433.70 at end of 40 years=	PV*(1+r)^n
	=	18433.70*(1+0.1)^40
	=	834,296
	The funds will be worth $834296 if you wait till age 61