Question

Company FM2 must pay 100,000 in 4 years. In order to fully immunize from changes in interest rate, the company invests in a 3 year zero coupon bond that matures for 45,000 and a 5 year zero coupon bond that matures for X. The actuary for Company FM2 determined that their portfolio fully immunized their ability to meet their obligations at the current interest rate i. Calculate i.

Answer 1

Answer:

5. 11.1%

Explanation:

the options for this question are missing:

1. 5%
2. 7.8%
3. 10%
4. 10.5%
5. 11.1%

I prepared the following equation:

$100,000 = $45,000(1 + i)³ + x(1 + i)⁵

There is something that we must remember about zero coupon bonds, and that is that they are sold in thousands. This equation is complex, but there is an easier way to solve it. We can plug in the options to determine which % will result in a possible answer.

The answer is 11.1%, since the other options resulted in numbers which are not even close to a thousand.

$100,000 = $45,000(1.111)³ + x(1.111)⁵

$100,000 = $61,709.88 + 1.2763x

$38,290.12 = 1.2763x

x = $38,290.12 / 1.2763 = $30,000