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I am trying to solve the following problem:

Debtor issued a bond on 20 000€ (including interest rate) with maturity rate of 8 months and interest rate of 8% per annum. Month later, the creditor sold the bond to a different person, who discount the bond with 9% interest rate p.a.

How much did the creditor receive for the bond?

My solution is the following:

$FutureValue$ $= P(1+i*t*t/12) = 20000(1+0,08*8*8/12) = 28533$

Is it correct? Thanks

Daniel P.
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  • What does the phrase "including interest rate" mean? I would assume that a $20000$€ bond at $8%$ would have a value of $20000(1+0.08\cdot8/12)=21066.67$€ in $8$ months, which is totally out of line with your answer. Why do you multiply $8/12$ by $8$? – saulspatz Sep 23 '19 at 17:08
  • The creditor must receive less than $20000$ because the higher interest rate will reduce the value. The future value should not be quadratic in $t$, and you want the present value. – Ross Millikan Sep 23 '19 at 17:09

2 Answers2

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Assume the creditor sold the bond one month after acquiring it, the creditor receives

$$ 20000 \times \frac{1+0.08\cdot \frac {8}{12} }{ 1+0.09\cdot \frac {7}{12} } = 20015.8$$

Quanto
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If the bond only pays at maturity, it pays $20000 +\frac 8{12} \cdot 8\% \cdot 20000$ at the end of $7$ months. You are expected to discount at $9\%$ per year back to present value.

Ross Millikan
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  • I'm not sure that's correct. I've never seen a bond that made monthly payments. In my experience, a bond with a term of less than a year would only pay interest at maturity. (My experience is old though, so maybe things have changed.) – saulspatz Sep 23 '19 at 17:25
  • @saulspatz: somehow I read the problem to pay monthly, but I don't see it now. I have updated – Ross Millikan Sep 23 '19 at 17:29