An automobile financier claims to be lending | vedclass

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(B) The financier calculates interest every six months,which means the interest is compounded semi-annually.Let the principal amount be $P = 100$.The

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$10.25$

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(B) The financier calculates interest every six months,which means the interest is compounded semi-annually.Let the principal amount be $P = 100$.The annual rate of interest is $10 \%$,so the semi-annual rate is $r = \frac{10}{2} = 5 \%$.For one year,there are two compounding periods.The amount after one year is $A = P(1 + \frac{r}{100})^n = 100(1 + \frac{5}{100})^2$.$A = 100(1.05)^2 = 100 	imes 1.1025 = 110.25$.The interest earned in one year is $110.25 - 100 = 10.25$.Therefore,the effective rate of interest is $\frac{10.25}{100} 	imes 100 = 10.25 \%$.

An automobile financier claims to be lending money at simple interest,but he includes the interest every six months for calculating the principal. If he is charging an interest of $10 \%$ per annum,the effective rate of interest (in $\%$) becomes:

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