Question

Jill has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Jill is employing a full immunization strategy using an annual effective interest rate of 5%. Calculate ∣A−B∣ A) 0 B) 146 C) 293 D) 586 E) 881

Answer 1

To calculate |A - B|, we need to find the values of A and B. Using the present value formula, we can calculate the present value of Jill's liability. Setting up equations for the present value of A and B, we can solve for their values. Finally, we can calculate |A - B|.

Step-by-step explanation:

To calculate |A - B|, we need to find the values of A and B. Let's start with the present value of Jill's liability. Using the formula for present value of a future payment: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods, we can calculate the present value of Jill's liability:

PV = 6000 / (1 + 0.05)^4 = 4563.26

Next, we can set up equations for the present value of A and B:

A / (1 + 0.05)^2 + B / (1 + 0.05)^6 = 4563.26

Now, let's solve for A and B:

A = 4563.26 * (1 + 0.05)^2 = 5250.85

B = (4563.26 - A * (1 + 0.05)^2) / (1 + 0.05)^6 = 4954.81

Finally, we can calculate |A - B|:

|A - B| = |5250.85 - 4954.81| = 296.04