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.
Write a professional memo that covers the following information: a.Explain to the client the main differences between simple interest versus compound interest.
b.Explain the results of the three different options by showing the client the step-by-step calculations.
c.Explain which investment option is better for your client and why.
1. P = Po(1+r)^n.
Po = $500,000.
r = (6%/4)/100% = 0.015 = Quarterly %
rate expressed as a decimal.
n = 4comp./yr. * 5yrs. = 20 Compounding
periods.
Plug the above values into the given Eq.
and solve for P.
2. P = Po(1+r)^n.
r = APR = (8%/100% = 0.08
n = 1comp./yr. * 5yrs. = 5 Compounding periods.
Calculate P.
3. P = Po + Po*r*t.
t = 10 yrs.
r = 0.145
1. P = Po(1+r)^n.
Po = $500,000.
r = (6%/4)/100% = 0.015 = Quarterly %
rate expressed as a decimal.
n = 4comp./yr. * 5yrs. = 20 Compounding
periods.
Plug the above values into the given Eq.
and solve for P.
2. P = Po(1+r)^n.
r = APR = (8%/100% = 0.08
n = 1comp./yr. * 5yrs. = 5 Compounding periods.
Calculate P.
3. P = Po + Po*r*t.
t = 10 yrs.
r = 0.145
Memo
Date: [Date]
To: [Client's Name]
From: [Your Name]
Subject: Investment Advice for Lottery Winnings
Dear [Client's Name],
I hope this memo finds you well. I have carefully reviewed the investment options presented to you by the three financial institutions. Below, I will explain the main differences between simple interest and compound interest, provide step-by-step calculations for each option, and offer my recommendation based on your circumstances.
a. Differences between Simple Interest and Compound Interest:
Simple Interest: Simple interest is calculated solely on the principal amount. It does not take into account any interest earned over time. The formula for calculating simple interest is: Interest = Principal x Rate x Time.
Compound Interest: Compound interest includes interest earned on both the initial principal amount and any accumulated interest over time. It is calculated based on compounding periods (such as quarterly or annually). The formula for calculating compound interest is: A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
b. Step-by-step Calculations for the Investment Options:
Option 1: 6% compounded interest quarterly for 5 years.
Using the formula for compound interest, we calculate the final amount as follows:
A = $500,000 * (1 + 0.06/4)^(4*5)
A = $500,000 * (1.015)^20
A = $500,000 * 1.348
A ≈ $674,032.93
Option 2: 8% compounded interest annually for 5 years.
Applying the compound interest formula:
A = $500,000 * (1 + 0.08/1)^(1*5)
A = $500,000 * (1.08)^5
A = $500,000 * 1.469
A ≈ $734,500
Option 3: 14.5% simple interest for 10 years.
Using the formula for simple interest:
Interest = $500,000 * 0.145 * 10
Interest = $725,000
c. Recommendation:
After performing the calculations, it is evident that Option 2, offering 8% compounded interest annually for 5 years, is the best choice for your investment. It provides the highest final amount of approximately $734,500.
The reason Option 2 outperforms the others is that compound interest allows for the reinvestment of interest earned over time, resulting in a higher return on investment. Both Option 1 (6% compounded interest quarterly for 5 years) and Option 3 (14.5% simple interest for 10 years) yield lower returns compared to Option 2.
I recommend selecting Option 2 for its higher compounding interest rate, which will maximize your investment growth over the next five years.
Please feel free to contact me if you have any further questions or require additional information. I am here to assist you in making informed investment decisions.
Best regards,
[Your Name]