Question

A $5000 bond maturing at 103 on 10/1/2008 had semiannual coupons at 6%.

Find the purchase price on 4/1/2001 to yield 6.2% compounded semiannually.

Assume that the above bond was sold on 6/22/2005. At what price must it have

been sold to yield the buyer the same 6.2%?

Answer 1

Firstly, we will calculate the Effective annual rate(EAR) of 6.2% compounded semi-annually.

EAR = ((1+(Interest rate/Number of compounding periods))^ number of compounding periods) -1

= ((1+(6.2%/2))^2) - 1

= 6.2961%

Time period =7 years.

Now we will use a BA 2 Plus Financial calculator to find the purchase price of the bond-

N(Number of coupon payments) = 7.5*2 = 15

I/Y(Interest rate per period) = 6.2961%/2 = 3.14805%

PMT(Coupon payment per period) = (6%*$5000)/2 = 150

FV(Face value) = $5000

CMPT PV

Purchase price = $4912.5684

The preset value can alternatively calculated using the following equation-
PV = CF / (1 + r/n) t*n
The calculated answer would be the same.

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