Final answer:
John Regan's annuity's future value after 6 years with a 6% interest rate compounded annually is calculated using the future value of an annuity formula. After plugging in the values and performing the calculation, the future worth of his investment can be found.
Step-by-step explanation:
John Regan made deposits of $790 at the end of each year for 6 years, with an interest rate of 6% compounded annually. To find the future value of Regan's annuity, we use the future value of an annuity formula:
FV = P × 【(】(1 + r)^n - 1】/r】
Where:
- FV is the future value of the annuity.
- P is the periodic payment amount.
- r is the annual interest rate (expressed as a decimal).
- n is the number of periods.
Plugging in the values we get:
FV = $790 × 【(】(1 + 0.06)^6 - 1】/0.06】 = $790 × 【(】1.06^6 - 1】/0.06】
Calculating the value inside the brackets and then multiplying by $790, we find the future value of his annuity after 6 years. Using a calculator, we can determine the final answer, making sure to round to the nearest cent, as the question requires.