Final answer:
The question involves calculating the present value of a series of $69 monthly payments for 8.25 years with a 10% annual interest rate compounded monthly. The formula for present value of an annuity is used to determine the amount that would need to be invested now to generate these payments over the specified period.
Step-by-step explanation:
The student is asking about the present value of an annuity, which is a series of equal payments made at regular intervals. To calculate the discounted value of $69.00 made at the end of each month for 8.25 years with an interest rate of 10% compounded monthly, we can use the formula for the present value of an annuity:
PV = Pmt × [ (1 - (1 + r)^(-n)) / r ]
Where PV is the present value, Pmt is the monthly payment amount, r is the monthly interest rate (annual interest rate divided by 12), and n is the total number of payments (months). Here's the calculation:
Pmt = $69.00
Annual Interest Rate = 10% or 0.10
Monthly Interest Rate (r) = 0.10 / 12
Total Number of Payments (n) = 8.25 years × 12 months/year
Using the above values in the formula gives us the present value which is the amount that would have to be invested now, at a 10% interest rate compounded monthly, to generate these $69 monthly payments for 8.25 years.