Question

Compare the investment below to an investment of the same principal at the same rate compounded annually.

​principal: ​$​7,000, annual​ interest: ​7%, interest​ periods: 2 ​, number of​ years: 11
After 11 years, the investment compounded periodically will be worth $_____ more than the investment compounded annually. (Round to two decimal places as needed.)

Answer 1

The investment compounded periodically will be worth $2,511.69 more than the investment compounded annually after 11 years.

Step-by-step explanation:

To compare the investment compounded periodically to the investment compounded annually, we need to calculate the future value of each investment after 11 years. For the investment compounded periodically, the principal is $7,000, the annual interest rate is 7%, and the interest periods are 2. Using the compound interest formula:

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

Calculating the future values:

For the investment compounded periodically: Future Value = $7,000 × (1 + (0.07 / 2))^(2 × 11) = $17,646.79

For the investment compounded annually: Future Value = $7,000 × (1 + 0.07)^11 = $15,135.10

The investment compounded periodically will be worth $17,646.79 - $15,135.10 = $2,511.69 more than the investment compounded annually after 11 years.