1a) You, along with 20 of your closest friends (at least until you collect your

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?

$1,000,000 if my discount rate is less than 6.5%

$75,000 for all discount rates

$75,000 yearly if my discount rate is less than 6.5%

$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?

$5,945

$7,310

$4,966

$9,655

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

6 years

4.5 years

5 years

7 years

$1,000,000 if my discount rate is less than 6.5%

$75,000 for all discount rates

$75,000 yearly if my discount rate is less than 6.5%

$1,000,000 for all discount rates

Explanation / Answer

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

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