Question

Suppose that Albert can buy a bond for $1,000 that matures in two years and pays Albert $1,102. 5 with certainty. Today he is indifferent between this bond and one that has some risk but on which the annual interest rate is 3% higher. How much, to the nearest penny, does the riskier bond pay in two years?

a. $1,166. 40

b. $1,160. 00

c. $1,168. 65

d. $1,169. 64

Answer 1

d

Step-by-step explanation:

To find the amount that the riskier bond pays in two years, we need to determine what interest rate Albert would require to be indifferent between the two bonds.

Let's assume that the riskier bond pays an interest rate of r. Then the amount that it pays in two years is given by:

1000 * (1 + r/100)^2

Since Albert is indifferent between the two bonds, this amount must be equal to $1,102.5.

So we have:

1000 * (1 + r/100)^2 = 1102.5

We can solve for r by taking the square root of both sides and multiplying by 100:

r = 100 * sqrt(1102.5 / 1000) - 100

r = 100 * sqrt(1.1025) - 100

r = 100 * 1.0498 - 100

r = 4.98

So the interest rate on the riskier bond must be 4.98%.

Finally, to find the amount the riskier bond pays in two years, we can use the formula:

1000 * (1 + 4.98/100)^2 = $1,169.64 (to the nearest penny).

Thus, the answer is d) $1,169.64.