Question

the 6-month,12-month,18- month, and 24- month zero rates are4%,4.5%, 4.75% and 5% with continouus compounding .
what are the rates with semi annual compounding ?

Answer 1

Formula for converting continuously compounded rate to semi annual rate

(1+r)=e^{^(rp*t)}

where r= semiannual rate of interest

e=2.7183 constant

rp=rate of pereiod given

t=1/number of semiannuals in the given period

(i) 6 month rate(rp)=4% or .04

1+r=2.7183^^.04*1

1+r=1.040811

r=.040811 or 4.0811% per semiannum

(ii)

1+r=2.7183^^.045*.5

1+r=1.022755

r=.022755 or 2.2755% per semiannum

(iii)

1+r=2.7183^^.0475*.3333

1+r=1.01596

r=.01596 or 1.596% per semiannum

(iv)

1+r=2.7183^^.05*.25

1+r=1.01258

r=.01258 or 1.258% per semiannum