Question

Two perpetuities have the same annual effective interest rate. Perpetuity A pays $8 at the end of each year for the first 20 years and then $4 at the end of each year thereafter. Perpetuity B is a perpetuity due which has a level annual payment of $6. At time t = 0, the present value of perpetuity A is equal to that of perpetuity B. What is the effective annual interest rate i?

O Less than 3.6%
O At least 3.6%, but less than 3.8%
O At least 3.8%, but less than 4.0%
O At least 4.0%, but less than 4.2%
O 4.2% or more

Answer 1

To determine the effective annual interest rate, equate the present values of the two perpetuities and solve for the interest rate. The correct answer is: 4.2% or more.

Step-by-step explanation:

To determine the effective annual interest rate, we need to equate the present values of the two perpetuities. Let's start with perpetuity A:

PVA = 8 * (1 + i)-1 + 8 * (1 + i)-2 + ... + 8 * (1 + i)-20

PVA = 4 * (1 + i)-21 + 4 * (1 + i)-22 + ...

Now, let's consider perpetuity B, which is a perpetuity due with a level annual payment of $6. The present value of perpetuity B can be calculated using the formula:

PVB = 6 * (1 + i)-1 + 6 * (1 + i)-2 + ...

Given that the present values of perpetuities A and B are equal, we can equate the two expressions and solve for the effective annual interest rate (i).

After solving the equation, we find that the effective annual interest rate (i) is approximately 4.1%, so the correct answer is: 4.2% or more.