Scenario: A client comes to you for investment advice on his $500,000 winnings from the lottery. He has been offered the following options by three different financial institutions and requests assistance to help understand which option would be the best for his investment.

Option 1: 6% compounded interest quarterly for 5 years.
Option 2: 8% compounded interest annually for 5 years.
Option 3: 14.5% simple interest for 10 years.

None of these is realistic today. Bank interest rates rarely go much over 1% a year.

Higher interest rates are risky and the investments may actually lose money.

http://www.nytimes.com/2013/02/02/business/a-prize-winning-plan-for-investing-when-interest-rates-are-low.html?_r=0

To determine which option would be the best for the client's investment, we need to calculate the final amount of money he would have after each option's specified time period. Let's go through the calculations for each option:

Option 1: 6% compounded interest quarterly for 5 years.
To calculate the final amount with compounded interest, we can use the formula: A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.

In this case, the principal amount (P) is $500,000, the annual interest rate (r) is 6%, the number of times compounded per year (n) is 4 (quarterly), and the number of years (t) is 5.

Calculating the final amount:
A = $500,000(1 + 0.06/4)^(4*5)
A = $500,000(1.015)^20
A ≈ $500,000 * 1.3498588
A ≈ $674,929.40

Option 2: 8% compounded interest annually for 5 years.
Using the same formula, the only difference is that the interest rate (r) is now 8% and the number of times compounded per year (n) is 1 (annually).

Calculating the final amount:
A = $500,000(1 + 0.08/1)^(1*5)
A = $500,000(1.08)^5
A ≈ $500,000 * 1.469328
A ≈ $734,664

Option 3: 14.5% simple interest for 10 years.
To calculate the final amount with simple interest, we can use the formula: A = P(1 + r*t), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years.

Calculating the final amount:
A = $500,000(1 + 0.145*10)
A = $500,000(1 + 1.45)
A = $500,000 * 2.45
A = $1,225,000

Now, comparing the final amounts:
Option 1: $674,929.40
Option 2: $734,664
Option 3: $1,225,000

Based on the calculations, it appears that Option 3 with a 14.5% simple interest for 10 years would provide the highest final amount of $1,225,000. However, it's important to note that this simple interest option does not compound like the other options. Consider discussing the pros and cons of each option with your client to better understand their investment goals and risk tolerance before making a decision.