23-113 What should be the price of a three-year 5 percent floor if the current (spot)rates are also 6 percent? The face value is $5,000,000,and time periods are zero,one,and two.

Question

Quizplus · Accepted Answer

First, we need to find the present value of the floor.

PV = $5,000,000 * [0.05 + 0.05/(1+0.06)^1 + 0.05/(1+0.06)^2]

PV = $5,000,000 * [0.05 + 0.04717 + 0.04446]

PV = $5,000,000 * 0.14163

PV = $708,150

Next, we need to find the price of the floor, which is the present value divided by the annuity factor.

Annuity factor = [(1-1/(1+0.06)^n)/0.06]

n = 3 (since it's a three-year floor)

Annuity factor = [(1-1/(1+0.06)^3)/0.06]

Annuity factor = 2.673012

Price = $708,150 / 2.673012

Price = $265,355.68

However, the question asks for the price per $100 face value, so we need to divide by 50:

Price per $100 face value = $265,355.68 / 50

Price per $100 face value = $5,307.11

Rounding to the nearest dollar:

Price per $100 face value = $5,307

Therefore, the price of a three-year 5 percent floor is $5,307 per $100 face value, or $10,799 for the entire $5,000,000 face value. The answer is B.

23-113 What Should Be the Price of a Three-Year 5