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A ?$10,000?, ?6% bond with? semi-annual coupons is redeemable at par
A ?$10,000?, ?6% bond with? semi-annual coupons is redeemable at par. What is the purchase price to yield? 7.5% compounded? semi-annually
?(a) nine years before? maturity?
?(b) fifteen years before? maturity?
Expert Solution
a) Computation of Purchase Price using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Purchase Price of Bond = ?
Rate = Yield to Maturity = 7.5%/2 = 3.75% compounded semiannually
Nper = Number of Periods to Maturity = 9 Years*2 = 18 Periods
PMT = Semiannual Coupon Payment = $10,000*6%/2 = $300
FV = Face Value = $10,000
Substituting the values in formula:
=-pv(3.75%,18,300,10000)
PV or Purchase Price of Bonds = $9,030.97
b) Computation of Purchase Price using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Purchase Price of Bond = ?
Rate = Yield to Maturity = 7.5%/2 = 3.75% compounded semiannually
Nper = Number of Periods to Maturity = 15 Years*2 = 30 Periods
PMT = Semiannual Coupon Payment = $10,000*6%/2 = $300
FV = Face Value = $10,000
Substituting the values in formula:
=-pv(3.75%,30,300,10000)
PV or Purchase Price of Bonds = $8,662.81
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