Question

1. On a recent trip to the united States, you purchased a ticket in a state lottery. Now you discover that you are the lucky winner of the $30 million prize. You can take your prize money either as (a) 30 payments of $1 million per year (starting today), or (b) $15 million paid today. If the interest rate is 8%, which option should you take. Show calculations

2. James has just turned 35 years old, and he has decided it is time to plan seriously for his retirement. On each birthday, beginning in one year and ending when he turns 65, he will save $10,000 in an RRSP account. If the account earns 10% per year, how much will James have saved at age 65.

Answer 1

Answer 01 :

Option 01 :

30 payments of $1 million per year (starting today) we will use the formula for an annuity due

So Present Value of All Payment

Here P = Annual Payment of $1 million per year  

r = 8% = 0.08

n = 30 Years

PVA = 12.158 Million

Option 02    $15 million paid today

Now Present Value of Option 01 is less than the PV of Option 02.

So Option 02 should be chosen. (Ans)

Answer 02 :

Current Age of James = 35 Years

Retirement Age = 65 Years

Compounding Period (n) = Retirement Age -  Current Age = 65 - 35 = 30 Years

He saves $10,000 in an RRSP account starting today.

r = 10% = 0.10

Future Value of Annuity Due ( Payment Starts at First of each year)

FVA = 10,000 * 164.45 * 1.1 = 18,09,434.25 = 18,09,434 (Ans)

Ans :  James have saved at age 65 will be  18,09,434 (Ans)