Question

Six years ago you purchased a $1,000 par bond with 13 years to maturity and a 6.5% semi-annual coupon at a price of $1,200. If the yield to maturity of the bond remained constant, what should be the price today?

Answer 1

At the time of purchase,

No of semi-annual coupon payments pending till maturity (N) = 26 {13 years x 2}

Semi-annual coupon payment (PMT) = $1000 x 6.50% / 2 = $ 32.50

Future value of bond (FV) = $1,000

Price of bond (PV) = {-$1,200}

Semi-annual yield to maturity (Y) = ??

Using financial calculator or Rate function in excel,

Semi-annual yield to maturity (Y) = 2.2282% per semi-annum

After 6 years,

No of semi-annual coupon payments pending till maturity (N) = 14 {7 years x 2}

Semi-annual coupon payment (PMT) = $1000 x 6.50% / 2 = $ 32.50

Future value of bond (FV) = $1,000

Semi-annual yield to maturity (I) = 2.2282% per semi-annum {Since it is given that yield to maturity remained constant}

Price of bond (PV) = ??

Using financial calculator or PV function in excel,

Price of Bond (PV) = $ 1,121.73

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