Calculate the Ratio of Liabilities Payment

What is the ratio of b/B in a liability payment schedule?

Given that Jia Wen has a liability of $5000 due in 5 years, will make a payment of $3000 in 2 years, and another payment of B in 5+b years using a full immunization strategy with an annual effective interest rate of 7%, what is the ratio of b/B?

Final answer:

The value of b/B is approximately 1.

Explanation:

To calculate the value of b/B, we need to use the concept of present value and the formula for calculating the present value of a future payment. The present value of a future payment is calculated by discounting the future payment using the annual effective interest rate.

Let's break down the given information:

• Jia Wen has a liability of $5000 due in 5 years.
• Jia Wen plans to make payments of $3000 in 2 years and B in 5+b years.
• The annual effective interest rate is 7%.

First, calculate the present value of the $3000 payment due in 2 years:

The present value of a future payment can be calculated using the formula:

Present Value = Future Payment / (1 + Interest Rate)^Number of Periods

Using the given values, we have:

Present Value = $3000 / (1 + 0.07)^2

Simplifying the calculation:

Present Value = $3000 / (1.07)^2

Present Value = $3000 / 1.1449

Present Value ≈ $2619.51

Next, calculate the present value of the final payment of B due in 5+b years:

Since the time period is given as 5+b years, we cannot calculate the exact present value without knowing the value of b. However, we can express the present value of the final payment as:

Present Value = B / (1 + 0.07)^(5+b)

Now, set up an equation using the present values of the two payments:

$2619.51 + Present Value of B = $5000

Solving for B:

Present Value of B = $5000 - $2619.51

Present Value of B ≈ $2380.49

Now, solve for b/B by rearranging the equation:

b/B = (5+b) / 5

Substitute the values:

b/B = (5+b) / 5 ≈ (5+0) / 5 = 1

Therefore, b/B ≈ 1.