Question

If the effective annual rate of interest is known to be 12% on a debt that has semi-annual payments, what is the annual percentage rate? Enter your answer as a percentage rounded to 2 DECIMAL PLACES. Do not include the percentage sign in your answer.

Answer 1

Solution:
	Annual percentage rate
	APR is   11.66                     in percentage terms
Working Notes:
	Effective Annual Interest Rate (EAR)
	EAR = (1 + (i/n))^n    -1
	i= Annual Percentage rate = ??
	n= 2               ( as the bond is semi-annual means interest is 2 times a year, so 2 is used)
	Effective Annual Interest Rate (EAR)=12%
	EAR = (1 + (i/n))^n    -1
	12% = (1 + (i/2))^2    -1
	(1 + (i/2)) = (1 + 12%)^(1/2)
	(1 + (i/2)) =1.058300524
	i=(1.058300524 -1) x 2
	i=0.116601048
	i=11.660%
	i=11.66%
	Annual percentage rate
Hence	APR is 11.66   in percentage terms
Please feel free to ask if anything about above solution in comment section of the question.