Final answer:
To find the amount a student must deposit today to receive $525 at the end of each month for 2 years at 7.8% interest compounded monthly, use the present value of an annuity formula. For the total interest paid, calculate the total payments and subtract the initial deposit.
Step-by-step explanation:
The question involves calculating the present value of an annuity because the student wishes to have a series of regular payments ($525) for a certain period (2 years) with a compound interest rate. To solve part (a), we use the present value of an annuity formula, which is PV = PMT × [(1 - (1 + r)^(-n)) / r], where PV is the present value (amount to deposit initially), PMT is the regular payment amount, r is the monthly interest rate (0.078 / 12), and n is the total number of payments (2 years × 12 months). Part (b) requires us to find the total amount of interest paid, which involves calculating the sum of all payments and subtracting the initial deposit found in part (a).
Part A - Initial Deposit Calculation:
The present value PV is what we need to find, where PMT = $525, r = 7.8% / 12 per month, and n = 24 months (2 years). Inserting these into the formula gives us the initial deposit amount required.
Part B - Total Interest Calculation:
The total amount received from the annuity is 24 payments of $525, which is a simple multiplication. We find the interest by subtracting the initial deposit from this total amount.