Final answer:
The future value of the annuity is calculated with the formula FV = P × ((1 + r)^n - 1)/r, where P is the periodic payment, r is the quarterly interest rate, and n is the total number of payments. After calculation, the obtained future value does not match the options, indicating a potential error in the options or a requirement for recalibration of inputs.
Step-by-step explanation:
The student's question involves calculating the future value of an ordinary annuity with deposits made quarterly and interest compounded quarterly over a period of 3 years. We are given that the quarterly deposit is $500 and the interest rate is 7% per annum. To solve this, we can use the future value of an annuity formula:
FV = P × rac{((1 + r)^n - 1)}{r}
Where:
- P is the periodic payment (quarterly deposit)
- r is the interest rate per period (quarterly)
- n is the total number of payments (number of quarters)
In our case, P = $500, r = 0.07/4 (since it's compounded quarterly), and n = 3 × 4 = 12 quarters. Thus, the future value is calculated as follows:
FV = 500 × rac{((1 + 0.0175)^12 - 1)}{0.0175} = $7,357.19
Note: The calculated value does not match any given options, which suggests a possible error in the provided options or the need to recheck the calculations and adjustments.