Question
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%, the effective rate of interest becomes
Answer: Option B
$$\eqalign{
& {\text{Let the sum be Rs}}{\text{.100}}{\text{}} \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.for first 6 months}} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 10 \times 1}}{{100 \times 2}}} \right) \cr
& = {\text{Rs}}{\text{. }}5 \cr
& {\text{S}}{\text{.I}}{\text{.for last 6 months}} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{105 \times 10 \times 1}}{{100 \times 2}}} \right) \cr
& = {\text{Rs}}{\text{. }}5.25 \cr
& So, \cr
& {\text{Amount at the end of 1year}} \cr
& = {\text{Rs}}{\text{.}}\left( {100 + 5 + 5.25} \right) \cr
& = {\text{Rs}}{\text{.}}\,110.25 \cr
& \therefore {\text{Effective rate}} \cr
& = \left( {110.25 - {\text{100}}} \right) \cr
& = 10.25\% \cr} $$
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$$\eqalign{
& {\text{Let the sum be Rs}}{\text{.100}}{\text{}} \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.for first 6 months}} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 10 \times 1}}{{100 \times 2}}} \right) \cr
& = {\text{Rs}}{\text{. }}5 \cr
& {\text{S}}{\text{.I}}{\text{.for last 6 months}} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{105 \times 10 \times 1}}{{100 \times 2}}} \right) \cr
& = {\text{Rs}}{\text{. }}5.25 \cr
& So, \cr
& {\text{Amount at the end of 1year}} \cr
& = {\text{Rs}}{\text{.}}\left( {100 + 5 + 5.25} \right) \cr
& = {\text{Rs}}{\text{.}}\,110.25 \cr
& \therefore {\text{Effective rate}} \cr
& = \left( {110.25 - {\text{100}}} \right) \cr
& = 10.25\% \cr} $$
Was this answer helpful ?
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