Question

An investor has the following liabilities:

$10,000 in 5 years
$5,000 in 7 years
$5,000 in 10 years
He wants to invest in 4 years and 10 years zero coupon bonds if i = 6%. How much will the face value be?
A. $8,805.22
B. $8,500.00
C. $8,650.35
D. $8,750.00

Answer 1

The face value of the zero coupon bonds will be $8,805.22 for the bond invested in 4 years and $8,650.35 for the bond invested in 10 years, resulting in a total face value of $17,455.57.

Thus, the correct option is A.

Step-by-step explanation:

To calculate the face value of the zero coupon bonds, we can use the formula:

Face Value = Future Value / (1 + Interest Rate)^n

For the first bond that will be invested in 4 years, the future value is $10,000 and the interest rate is 6%. Using the formula, we have:

Face Value = $10,000 / (1 + 0.06)⁴ = $8,805.22

For the second bond that will be invested in 10 years, the future value is $5,000 and the interest rate is 6%. Using the formula, we have:

Face Value = $5,000 / (1 + 0.06)¹° = $8,650.35

Therefore, the total face value of the bonds will be $8,805.22 + $8,650.35 = $17,455.57

Therefore, the correct option is A. $8,805.22.