Final answer:
To calculate the discounted value of quarterly payments of $1387.00 over 10 years at an annual interest rate of 9% compounded monthly, apply the present value of an annuity formula. Round the final answer to the nearest cent and use a financial calculator or software for computation.
Step-by-step explanation:
To find the discounted value of $1387.00 paid at the end of every three months for 10 years at a 9% annual interest rate compounded monthly, we use the present value of an annuity formula. The quarterly payment is $1387.00, the interest rate per quarter (i) is 9% per annum compounded monthly, which is 0.09 / 12 * 3 = 0.0225 per quarter, and there are 4 payments per year over 10 years, meaning n = 40 total payments.
Using the present value of an annuity formula:
PV = Pmt * [(1 - (1 + i)^(-n)) / i]
Where:
- PV = Present Value
- Pmt = Quarterly Payment ($1387.00)
- i = Quarterly Interest Rate (0.0225)
- n = Total Number of Payments (40)
First, we calculate (1 + i)^(-n), round to six decimal places, then substitute the values into the formula and calculate the present value.
Without the actual computational values provided in the question, one can use a financial calculator or software to find the final present value by rounding the final answer to the nearest cent.