Final answer:
The present value that will generate a future value of $4,472, compounded quarterly at a 10 3/4% interest rate over 6 years, is approximately $2,193.49.
Step-by-step explanation:
To find the present value that will generate a future value of $4,472 at an interest rate of 10 3/4% compounded quarterly for 6 years, we use the formula for present value:
Present Value = Future Value / (1 + (interest rate / number of compounding periods))(number of compounding periods × time in years)
First, we convert the annual interest rate of 10 3/4% to a decimal: 10.75% = 0.1075. Since the compounding is quarterly, there are 4 periods per year. Thus:
Present Value = $4,472 / (1 + (0.1075/4))(4×6)
To find the exact present value, we do the calculation:
Present Value = $4,472 / (1 + 0.026875)24
Using a calculator:
Present Value = $4,472 / (1.026875)24 ≈ $4,472 / 2.039887 ≈ $2,193.49
The present value that will generate the future value of $4,472 is approximately $2,193.49 when compounded quarterly at an interest rate of 10 3/4% over 6 years.