Find the effective rate of interest corresponding to the nominal rate of 8% p.a. if it is converted to half yearly

Answer 1

let the effective semi-annual rate be j

(1+j)^2 = 1.08
1+j = √1.08 = 1.03923
j = .03923
2j = .07846
so the effective annual rate compounded semi-annually
= 7.846%

check:
on $1000, the amount after 1 year at 8% per annum
= 1000(1.08) = 1080
on $1000, the amount after 1 year at 7.846% compounded semi-annually
= 1000(1.03923)^2 = 1080