Question

View an exampleCompare the investment below to an investment of the same principal at the same rate compounded annually. principal: $3,000, annual interest: 9%, interest periods: 12, number of years: 16 After 16 years, the investment compounded periodically will be worth $ 1230.23 more than the investment compounded annually. (Round to two decimal places as needed.)compound interest

Answer 1

Sure, let's compare the two investments!

For the investment compounded annually with a principal of $3,000, an annual interest rate of 9%, and a number of years of 16, we can calculate the future value using the formula:

Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

Let's calculate the future value for the investment compounded annually:

Future Value = $3,000 * (1 + (0.09 / 1))^(1 * 16)
Future Value = $3,000 * (1 + 0.09)^16
Future Value ≈ $8,235.05

Now, for the investment compounded periodically, we know that after 16 years, it will be worth $1,230.23 more than the investment compounded annually. So, we can calculate the future value for the investment compounded periodically:

Future Value = $8,235.05 + $1,230.23
Future Value ≈ $9,465.28

Therefore, the investment compounded periodically will be worth approximately $9,465.28 after 16 years, which is $1,230.23 more than the investment compounded annually.