Final answer:
The future value of an annuity due with $700 quarterly payments for 6 years at a 12% annual interest rate compounded quarterly is calculated using the annuity due formula. After plugging in the values and solving, the final rounded amount represents the value of the annuity at the end of the period.
Step-by-step explanation:
To calculate the future value of an annuity due, we need to adjust the formula for a standard annuity to account for the fact that payments are made at the beginning of each period. The formula is FV = P * [((1 + r)^nt - 1) / r] * (1 + r), where P is the periodic payment, r is the periodic interest rate, n is the number of times interest is compounded per year, t is time in years, and FV is the future value of the annuity due.
In this case, we have:
- Quarterly payment (P) = $700
- Annual interest rate = 12%, so quarterly interest rate (r) = 12% / 4 = 3% or 0.03
- Number of quarters (nt) = 6 years * 4 quarters/year = 24 quarters
First, calculate the future value using the annuity due formula:
FV = 700 * [((1 + 0.03)^24 - 1) / 0.03] * (1 + 0.03)
Then, solve for FV, which is the final answer, rounding to the nearest cent.