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.
Compound interest
P is the principal (the initial amount you borrow or deposit)
r is the annual rate of interest (percentage)
n is the number of years the amount is deposited or borrowed for.
A is the amount of money accumulated after n years, including interest.
When the interest is compounded once a year:
A = P(1 + r)^n
Simple Interest
A = (r/100 * P )n
To determine which option would be the best for the client's investment, we need to calculate the future value of each option. The future value is the amount of money the client would have at the end of the investment period.
For Option 1, we will use the formula for compound interest, which is given by:
Future value = Principal * (1 + (interest rate / number of compounding periods)) ^ (number of compounding periods * number of years)
In this case, the principal amount is $500,000, the interest rate is 6%, and the compounding periods are quarterly (4 times a year). The number of years is 5. Plugging in these values into the formula, we have:
Future value = $500,000 * (1 + (0.06 / 4)) ^ (4 * 5) = $500,000 * (1.015) ^ 20
For Option 2, the interest is compounded annually, so we can use the same formula but with a compounding period of 1 and an interest rate of 8%. Plugging in the values, we have:
Future value = $500,000 * (1 + (0.08 / 1)) ^ (1 * 5) = $500,000 * (1.08) ^ 5
For Option 3, the interest is simple interest, which means it is not compounded. The formula for simple interest is given by:
Future value = Principal * (1 + interest rate * number of years)
Plugging in the values, we have:
Future value = $500,000 * (1 + (0.145 * 10))
Now, we can calculate the future value for each option and compare them to determine which one is the best investment option.