Assuming that the market is arbitrage-free, if a three-month zero-coupon bond yields 2.25 percent sign, a six-month zero-coupon bond yields 2.45 percent sign, a nine-month zero-coupon bond yields 2.95 percent sign, and a one-year zero-coupon bond yields 3.35 percent sign. What should the price of a one-year $ 1000 space space space 5 percent signpar-value bond with quarterly coupons

Question

Business

Livia

21 November, 16:43

Assuming that the market is arbitrage-free, if a three-month zero-coupon bond yields 2.25 percent sign, a six-month zero-coupon bond yields 2.45 percent sign, a nine-month zero-coupon bond yields 2.95 percent sign, and a one-year zero-coupon bond yields 3.35 percent sign. What should the price of a one-year $ 1000 space space space 5 percent signpar-value bond with quarterly coupons

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Answers (1)

Know the Answer?

Virginia Haas · Answer 1

The answer is 1016.69

Explanation:

Solution

Given that:

Coupon payment = 1000 * 0.05 / 4 = 12.5

Now,

The cash flow at

Rate Discount factor

3 months = 12.5 2.25% 1/1 + (0.0225/4) = 0.9944

6 months = 12.5 2.45% 0.9897

9 months = 12.5 2.95% 0.9789

I year = 12.5 3.35% 0.9676

Now,

The present value =

12.5 * (0.9944 + 0.9897 + 0.9789)

+

1012 * (0.9676 = 1016.69