Question

Economy

A $1,000 bond will mature in 10 years. The annual rate of interest is 6% payable semi annually. If compounding is semi annual and the bond can be purchased for $870, what is the yield to maturity in terms of the effective annual rate earned? Indicate the bond's current yield. Please answer in detail and include cash flow diagram

Answer 1

The bond price and yield to maturity are related as follows

Semi-annual interest payment = ( 6%/2) * $ 1000

Semi-annual interest payment = $ 30

$ 870 = $ 30 * PVIFA _{r =r/2 ? , n = 2n ( 20 years)} + $ 1000 * PVIF _{r = r/2, n = 2n ( 20 years)}

Calculting the value of r by trial and error

Yield to maturity = 2.04%

Current yield = $ 30 / $ 870

Current yield = 3.45%

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Cash flow diagram