**No Excel, Show all work. BA 2 Plus Financial Calculator allowed. John buys a 1

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**No Excel, Show all work. BA 2 Plus Financial Calculator allowed.

John buys a 10 year 1000 par value bond with semiannual coupons paid at an annual rate of 5%. The price of the bond assumes an annual nominal yield of 5% compounded semiannually. As John receives each coupon, he deposits the money in an account earning interest at an annual effective rate of i. At the end of 10 years he receives the final coupon payment and the redemption value of the bond (assumed to be the face value). He finds that he has earned an effective annual yield of 6% on your investment. Find i.

Explanation / Answer

Par Value = $1,000
Annual Coupon Rate = 5%
Semi-annual Coupon Rate = 2.50%
Semi-annual Coupon = 2.50%*$1,000 = $25.00
Annual Nominal Yield = 5%
Semi-annual nominal Yield = 2.50%
Semi-annual period to maturity = 20 (10 years)

Semi-annual nominal Yield is equal to the semi-annual coupon rate, so, current price of bond is $1,000

PV = 1000
FV = 1000
PMT = 25
N = 20
I (Semi-annual Yield) = 2.50%

Annual Effective Yield = (1 + Semi-annual Yield)^2 - 1
Annual Effective Yield = (1 + 0.025)^2 - 1
Annual Effective Yield = 1.025^2 - 1
Annual Effective Yield = 1.0506 - 1
Annual Effective Yield = 0.0506
Annual Effective Yield = 5.06%

So, i = 5.06%

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