Final answer:
To calculate the future value of the annuity, you divide the annual interest rate by four to get the quarterly rate, convert it into decimal form, calculate the total quarters in four years, and then substitute these into the future value formula for an annuity. The resulting future value of the $750 quarterly deposit at 6.8% for 4 years is approximately $13,358.18.
Step-by-step explanation:
To determine the future value of the annuity where $750 is deposited quarterly at an interest rate of 6.8% for 4 years, we use the future value formula for an annuity:
Future Value of Annuity = Payment × {[(1 + interest rate per period)^(number of periods) - 1] / (interest rate per period)}
Firstly, since the deposits are quarterly, the annual interest rate of 6.8% must be divided by the number of quarters in a year:
Interest rate per quarter = 6.8% / 4 = 1.7%
Convert the interest rate into decimal form for the calculation:
Interest rate per quarter (decimal) = 0.017
The total number of periods (quarters) in 4 years is:
Total quarters = 4 years × 4 quarters/year = 16 quarters
Now we plug these values into the formula:
Future Value of Annuity = $750 × {[(1 + 0.017)^16 - 1] / 0.017}
Performing the calculations:
Future Value of Annuity = $750 × {[(1.017)^16 - 1] / 0.017}
Future Value of Annuity = $750 × {[1.302776 - 1] / 0.017}
Future Value of Annuity = $750 × 17.8109
Future Value of Annuity = $13,358.18 (approx)
The future value of the $750 annuity deposited quarterly at a 6.8% interest rate for 4 years is approximately $13,358.18.