Jim has received an amazing grand prize offer in the mail. The contest rules req

Question

Jim has received an amazing grand prize offer in the mail. The contest rules require that he pre select one of two payment options. A single lump sum payment or an annual payment for each of 25 years. I hope he wins and that you advise him correctly.

A)     If we assume an annual interest rate of 8% for this analysis and that he desires the option with the greatest value today. Which option should he choose?

(Please show all work)

B)      At what interest rate dose he become equally attracted to each of the 2 options?

(perform linear interpolation if necessary)

THE CAPITAL PLAN - IMMEDIATE FINANCIAL SECURITY BENIFITS: PRIZE PAID OUT IN: One (1) payment of $833,337.00. FINANCIAL GOAL: Maximum capital pay out. BENEFIT: Allow for immediate access to maximum amount of money. IDEAL FOR: This payment plan is good for those who would like to eliminate outstanding debt immediately. Such needs might include credit/charge card balances home morlgages, busiiness loans, college loans, etc. YOU MUST INDICATE YOUR PREFERRED FORM OF PAYMENT. SELECT EITHER PAYMENT OPTION 1 OR PAYMENT OPTION 2. THE GROUTH PLAN - LOAN TERM FINANCIAL SECURITY BENEFETS: PRIZE PAID OUT IN: Twenty-Five (25) Annual Payments Of $66,667.00. FINANCIAL GOAL: Long-term security and grouth of principal. BENEFIT: Allows for controlled growth of principal over long period of time. IDEAL FOR: This payment plan is ideal for those seeking regularly scheduled additional income for a period of 25 years. The key feature is growth over time. Simply romove the seal of your choice shown above, then affix it to the appropriate space on the enclosed Grand Prize Payment Option Card enclosed.

Explanation / Answer

A) Present value of Option 1 = $833,337

Present value of Option 2 = 6667+ 6667/1.08 +  6667/1.08^2 +  6667/1.08^3 ...... 6667/1.08^24 =$768,587.73

Since present value of Option 1 is higher, he should choose Option 1

B)Let interest rate be r

Present value of Option 1 = Present value of Option 2

833,337 =6667+ 6667/(1+r) +  6667/(1+r) ^2 +  6667/(1+r) ^3 ...... 6667/(1+r) ^24

By trial and error

r= 6.13%

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