Final answer:
The future value of 15 deposits of $6,800 each, compounded at 8%, is calculated using the future value of an annuity due formula. After determining the future value interest factor (FVIF), it is multiplied by the payment and compounded once more. The final result is rounded to two decimal places according to the instructions.
Step-by-step explanation:
To calculate the future value of 15 deposits of $6,800 each made at the beginning of each period and compounded at an 8% annual interest rate, we use the future value of an annuity due formula:
FV = P × { [(1 + r)^n - 1] / r } × (1 + r)
Where:
FV is the future value of the annuity due,
P is the payment amount per period ($6,800),
r is the interest rate per period (8% or 0.08), and
n is the total number of payments (15).
First, we calculate the future value interest factor (FVIF) and round it to five decimal places:
FVIF = [(1 + 0.08)^15 - 1] / 0.08
After calculating the FVIF, we multiply it by the payment ($6,800) and compound it by the interest rate for one more period:
Future value = $6,800 × FVIF × (1 + 0.08)
Finally, we round the final future value to two decimal places as requested.