Final answer:
Calculations of the present value of different annuity streams involve applying the present value formula for annuities. The formula needs to be adjusted for the compounding period and the timing of payments (end of period or beginning). Specific conditions like annual or quarterly payments and compounding require a tailored approach to the interest rate and number of periods.
Step-by-step explanation:
The subject in question deals with the calculation of the present value of annuity streams under various conditions: annual payments with annual compounding, quarterly payments with quarterly compounding, and quarterly payments made at the beginning of the period with quarterly compounding. Each scenario requires the application of the present value formula for annuities, considering the different compounding periods and whether the payments are made at the beginning or the end of each period.
For the first scenario (a), the present value of an annuity can be found using the formula:
Present Value = Pmt [(1 - (1 + r)^-n) / r]
Where Pmt is the payment amount ($4,000), r is the interest rate (5% or 0.05), and n is the total number of periods (4 years).
For the second scenario (b), since the payments are made quarterly and the compounding is quarterly, the interest rate per period needs to be adjusted to a quarterly rate, and the number of periods should reflect the total number of quarters.
In the third scenario (c), the calculation is similar to (b), but an additional factor accounts for the fact that the payments are made at the beginning of each period, known as an annuity due.