To fund its wars against Napoleon, the British government sold console bonds. Th

Question

To fund its wars against Napoleon, the British government sold console bonds. There were referred to as "perpetuities" because they would pay 3 every year in perpetuity (forever). If a citizen could purchase a console for 25, what would its annual interest be? What if the price were 50? 100? Bonds are known as fixed income securities because the future payments that they will make to investors are fixed by the bond agreement in advance. Do the interest rates of bonds and other investments offer fixed future payments vary positively or inversely with their current prices?

Explanation / Answer

pv =3/(1+r)^n from n=0 to infiity

PV = 3/(1-(1+r)) = 3/r

25 = 3/r

r = 3/25 = .12 = 12%

for PV = 50

r = 3/50 = .06 =6%

for 100

r = 3/100 = .03 = 3%

aas it is evident from the above example fixed future payments vary inversely with their current prices

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