Final answer:
The question involves calculating the future value and interest of an annuity where $100 is deposited annually at a 4% interest rate, compounded annually, over 7 years. The future value is calculated using the annuity formula, and interest earned is the difference between the future value and the total deposits.
Step-by-step explanation:
The subject of this question is to calculate the future value of an annuity and the interest earned. An annuity is a series of equal payments made at regular intervals. In this case, the payments are $100 at the end of each year, the interest rate is 4% compounded annually, and the time is 7 years. To find the future value of the annuity, we use the formula for the future value of an ordinary annuity:
Future Value = P × ((1 + r)n - 1) / r
where P is the periodic deposit, r is the interest rate per period, and n is the number of periods. Plugging in our values we get:
Future Value = $100 × ((1 + 0.04)7 - 1) / 0.04
Calculating the above, we find the future value of the annuity. To find the total interest earned, we deduct the total deposits made over the 7 years from the future value of the annuity:
Interest Earned = Future Value - (Periodic Deposit × Number of Periods)