excans:6d1c25b57c: Difference between revisions

Latest revision as of 21:13, 20 November 2023

Solution: C

Let A be the redemption value of the zero-coupon bonds purchased and B the number of two- year bonds purchased. The total present value is:

[[math]] 1783.76=A/1.05+B(100/1.06+1\,100/1.06^{2})=0.952384+1073.3357B. [[/math]]

To exactly match the cash flow at time one, A + 100B = 1000. Substituting B = 10 – 0.01A in the first equation gives 1783.76 = 0.95238A + 10733.357 – 10.733357A for A = 8949.597/9.780977 = 915. The amount invested is then 915/1.05 = 871.

@@ Line 1: / Line 1: @@
-'''Solution: B'''
+'''Solution: C'''
-The company must purchase 4000 in one-year bonds and 6000 in two-year bonds. The total purchase price is 4000 /1.08 + 6000 /1.11<sup>2</sup>= 8573.
+Let A be the redemption value of the zero-coupon bonds purchased and B the number of two-
+year bonds purchased. The total present value is:
+<math display = "block">
+.76=A/1.05+B(100/1.06+1\,100/1.06^{2})=0.952384+1073.3357B.
+</math>
+To exactly match the cash flow at time one, A + 100B = 1000. Substituting B = 10 – 0.01A in the first equation gives 1783.76 = 0.95238A + 10733.357 – 10.733357A for A = 8949.597/9.780977 = 915. The amount invested is then 915/1.05 = 871.
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