maths problem plz help?

Question

mathematics problem plz help.
the debentureholder of a co receive int @10%p.a payable half-yearly on 30 june and 31 dec and an additional int @2%p.a .
payable annually on 31 dec each yr. if an investor purchase one debenture of Rs. 100 for Rs.90 on jan find his yield expressed as an effective rate of interest per half year.What would be the yield p.a.

this prob is of mathematics if any one can help me out in this regard.

plz helpthnax in advance

Answer 1

the effective rate of the two semi-annual interest payments is

(1+0.10/2)^2-1=0.1025 adding the additional interest rate we get annual coupon payments at year-end of 12.25

the payments are based on face value of 100 and it only cost 90

so we have a perpetuity of 90=12.25/r, r is the yield

or r=12.25/90=13.61%