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Homework answers / question archive / A $5000 bond with a coupon rate of 6

A $5000 bond with a coupon rate of 6

Finance

A $5000 bond with a coupon rate of 6.4% paid semi-annually has four years to maturity and a yield to maturity of 6.2%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?

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First we calculate Price of Bond before Changes:

Computation of Bond's Price using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,
PV = Bond Price = ?

Rate = 6.2%/2 = 3.1% compounded semiannually

Nper = 4 Years * 2 = 8 periods

PMT = $5,000*6.4%/2 = $160

FV = $5,000

Substituting the values in formula:

=-pv(3.1%,8,160,5000)

PV or Bond's Price = $5,034.95

 

Now we calculate Price of Bond after Changes:
Computation of Bond's Price using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,
PV = Bond Price = ?

Rate = (6.2%-0.8%)/2 = 2.7% compounded semiannually

Nper = 4 Years * 2 = 8 periods

PMT = $5,000*6.4%/2 = $160

FV = $5,000

Substituting the values in formula:

=-pv(2.7%,8,160,5000)

PV or Bond's Price = $5,177.73

 

So, Change in price of bond = 5177.73 - 5034.95
                                                   = 142.78

Hence, the price rise by $142.78.

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