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HW__8_Solutions_-_Part_1

# HW__8_Solutions_-_Part_1 - Solutions to Supplemental...

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1. A \$1 , 000 10% 10-year bond is purchased at issue for \$880 and is redeemable for \$1 , 020 . Find the yield rate for this bond (expressed as a nominal annual rate, convertible semi- annually). Solution: Using calculator functions (1020 FV -880 PV 50 PMT 20 N CPT I/Y) gives a semi-annual eﬀective yield rate of 6.10925%, multiply this by 2 to get i (2) = 12 . 2185% . 2. A 12% bond with a face amount of \$6 , 000 will mature in 10 years. If the annual nominal yield rate, convertible semi- annually, for this bond is 6%: (a) how much of a premium was this bond bought at? (i.e., what is the diﬀerence between the purchase price and the face amount?) Solution: Using calculator functions (6000 FV 360 PMT 3 I/Y 20 N CPT PV) gives a purchase price (present value) of \$8 , 677 . 95, which is \$2 , 677 . 95 greater than the face amount. Alternatively, you can use the premium-discount formula: amount of premium = P - F = F ( r - j ) a n j = 6000(0 . 06 - 0 . 03)

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HW__8_Solutions_-_Part_1 - Solutions to Supplemental...

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