Question

Consider a 22-year annuity-immediate with payments of 3,6,9, ..., 66. Which of the following formulas gives the PV (Present Value) of this annuity?

Options:
A) PV = 3 × ((1 - (1 + r)^(-22)) / r)
B) PV = 3 × ((1 + r)^22 - 1) / r
C) PV = 3 × ((1 + r)^(-22) - 1) / r
D) PV = 3 × ((1 - (1 - r)^22) / r)

Answer 1

The correct formula to calculate the present value (PV) of the given annuity is option A) PV = 3 × ((1 - (1 + r)^(-22)) / r).

Step-by-step explanation:

The correct formula to calculate the present value (PV) of the given annuity is option A) PV = 3 × ((1 - (1 + r)^(-22)) / r).

Here is a step-by-step explanation:

1. Calculate the discount factor using the formula (1 + r)^(-n), where r is the interest rate and n is the number of periods (in this case, 22).
2. Substitute the discount factor into the formula: PV = R × ((1 - discount factor) / r), where R is the value of each payment (in this case, 3).
3. Calculate the final present value by multiplying R and the result from step 2.