Question

1a) You, along with 20 of your closest friends (at least until you collect your winnings), have won the lottery. Now comes the hard part; determining how to collect the winnings. The next question is typical when making this choice.

You are offered your choice of after-tax proceeds: $1,000,000 now or $75,000 each year for 30 years. Which is your choice given your expectation of inflation and interest rates (i.e. your discount rate) over the period?

	a.	$1,000,000 if my discount rate is less than 6.5%
	b.	$75,000 for all discount rates
	c.	$75,000 yearly if my discount rate is less than 6.5%
	d.	$1,000,000 for all discount rates

1b) You are saving up for your child's college education, and have concluded that when she is 18 (in 8 years - yipes!) you will need $75,000. Luckily your aunt has put away a $10,000 bond that will mature at that time. In the meantime, the bond's return is 5% after taxes (assume that the interest payments are not reinvested). If your expected rate of return is 7%, how much will you need to save at the end of each year to meet your goal?

	a.	$5,945
	b.	$7,310
	c.	$4,966
	d.	$9,655

1c) Using the Rule of 72, approximately how long will it take to double your money if you invest it at 14%?

	a.	6 years
	b.	4.5 years
	c.	5 years
	d.	7 years

Answer 1

1. a) option c)$75,000 yearly if my discount rate is less than 6.5% is the correct option because

PV of annuity at 6.5% = Annuity * ( 1 -( 1+r)^-n)/r =75000 * ( 1 -( 1+6.5%)^-30)/6.5% = 979,400.69
However for PV of annuity at 6% = Annuity * ( 1 -( 1+r)^-n)/r =75000 * ( 1 -( 1+6%)^-30)/6% = 1032362.34

In scond case PV of annuity is higher than 1,000,000
Hence interest rate should be less than 6.5% for choosing annuity.

1 b) Amount received through bond =Par value + 8 * Coupon = 10,000 + 8 * 10,000 * 5/100 = 14,000
The amount required at end of 8 years = 75,000 - 14,000 = 61,000
The amount to be saved daily = PMT
PMT* (( 1+r)ⁿ -1)/r = 61,000
PMT*((1+7%)⁸ -1)/7% = 61,000
PMT * 10.2598 = 61,000
PMT = 5945
So option a is correct.
1c) Acoording Rule of 72
No of years when amount will double = 72/14 = 5.143
So it will take 6 years to double because in 5th year it would not be double