Question

1.   You have just received some great news from your parents… they are going to give your inheritance early, starting now! But, they’re going to force to you make a decision on how you want it. At the end of the day, they are going to give you a total of $500,000. But you have to pick one of the two options for disbursement:

Option A: You get it in three lump sum payments as follows:
•   You receive $100,000 right now.
•   At the end of year 10, you get $100,000.
•   At the end of year 20, you get $300,000.

Option B: You get monthly installments throughout, as follows:
•   Starting at the end of the current month, you will receive $1,200 per month for the next 10 years.
•   After that, you will receive $1,483.33 per month for the following 20 years.

The interest rate is an APR of 6%, compounded monthly, for both scenarios. You have decided that you will choose the one that is worth the most to you in today’s money. Which would you choose (fill in the following)? (20 pts)

   Option A Value: ____________

   Option B Value: ____________

   The better option: ___________
 

Answer 1

Interest rate = 6% compounded monthly = 6%/12 or 0.5% per month

Option A:

Present value = 100000 + 100000/(1+0.5%)^(12*10) + 300000/(1+0.5%)^(12*20) = $245,592.12

Option B

Present value of $1200 per month for 10 years = (1200/0.5%)*(1-1/(1+0.5%)^(12*10)) = $108088.14

Present value of $1483.33 per month for 10 years = (1/(1+0.5%)^10)*(1483.33/0.5%)*(1-1/(1+0.5%)^(12*20)) = $196,971.21

Total present value = $108088.14 + $196,971.21 = $305,059.36

Option A value = $245,592.12

Option B value = $305,059.36

Option B is better