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This is the question and solution provided by the Uni. Im not sure how they...

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Finance

This is the question and solution provided by the Uni. Im not sure how they determined the present value of the $103 payment to be 97.09. Please explain how this works.
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2(b) [10 marks] A six-month $100 zero-coupon government bond is currently selling for $97 and a one-year $100 government bond with a coupon rate of 6% is currently selling at par value. You are a government contractor and will receive a $100 payment from government one year from now. What is the present value of that payment? First, we know that the present value of a dollar to be received six months from now is 97 cents. Also, we know that the present value of the one-year coupon bond is $100. This bond will pay a $3 coupon six months from now. That coupon has a present value of 0.97x3=2.91. The coupon bond also pays $103 one year from now. The present value of that payment must be 100-2.91=97.09. That implies that the one-year zero coupon rate is: 103 (1+r) 97.09 in which case the one-year rate is 6.0871%. Consequently, your payment is worth: 100 (1.060871) 94.26

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