Question : The effective annual Rate of Interest corresponding to a nominal rate of interest of 13% per annum payable half-yearly is:
Option 1: 26%
Option 2: 26.85%
Option 3: 13%
Option 4: 13.42%
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Correct Answer: 13.42%
Solution : Rate of interest per annum = 13% Rate of interest half yearly = $\frac{13}{2}\%$ Use: Single equivalent increase = $(a+b+\frac{a×b}{100}$)%, where $a$% and $b$% are successive percentage change. $\therefore$ The effective rate of interest for one year when interest is counted half yearly = $\frac{13}{2}+\frac{13}{2}+\frac{\frac{13}{2}\times\frac{13}{2} }{100}$ = 13 + 0.42 = 13.42% Hence, the correct answer is 13.42%.
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