T-bond math, explain the first 2 answers ?

(a) The bond pays 5% of its face value each year. That amount is ...

  0.05 × $14,000 = $700 . . . . per year

So, in 6 years, the bond pays ...

  6 × $700 = $4200

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(b) The bond continues to pay $700 per year for the next 24 years. At the end of that time, the face value of the bond is also paid. So, the total amount paid to the bondholder in 24 years is ...

  24 × $700 + 14,000 = $16,800 +14,000 = $30,800

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(c) The present value of the bond is the present value of the cash flows it will generate. It will pay $700 at the end of each year for 24 years, then $14,000 at the end of the 24th year. Assuming cash flows are discounted at 7.5% per year over that period, the present value will be ...

  present value of series of payments = (700/1.075)·(1.075^-24 -1)/(1.075^-1 -1)

  ... = 7688.08

  present value of final payment = 14,000·1.075^-24 = 2467.88

So, the total present value is ...

  present value of the bond = $7,688.08 +2,467.88 = $10,155.96

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