Final answer:
To find the final amount from a $750 deposit at the beginning of each four-month period over ten years with 5% interest compounded quarterly, we use the future value of an annuity formula. We calculate for 30 periods and a quarterly interest rate of 5%/4 to determine the matching final amount.
Step-by-step explanation:
To solve the question 'If $750 is paid at the beginning of each four-month period for ten years at 5% compounded quarterly, what is the final amount?', we can use the future value of an annuity formula which accounts for regular deposits and compound interest. This is a type of problem commonly found in finance or business mathematics. First, we'll need to calculate the number of periods (n) and the periodic interest rate (r).
Since the payments are quarterly and the period is ten years, we have 10 years * 3 periods/year = 30 periods. The interest rate is compounded quarterly, so the periodic interest rate is 5% per year or 5%/4 per period. By plugging these values into the future value of an annuity formula: FV = P * [(1 + r)^n - 1] / r, where P is the payment, r is the periodic interest rate, and n is the number of periods, we can determine the final amount.
Calculating directly we would find the option that matches the result of the calculation to be the right answer. It is notable that this type of question requires careful consideration of the timing of payments and the frequency of compounding to ensure accurate results.