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%, find the effective rate of interest.

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Solution

Let the sum be Rs 100 then
SI for first 6 months = Rs $\frac{100 \times 10 \times 1}{100 \times 2} = R s 5$
SI for last 6 months = Rs $\frac{102 \times 10 \times 1}{100 \times 2} = R s 5.25$
So smount at the end of 1 year
= Rs $(100 + 5 + 5.25) = R s 110.25$
Rate = $110.25 - 100 = 10.25$ %

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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%, find the effective rate of interest.

Let the sum be Rs 100 thenSI for first 6 months = Rs 100×10×1100×2=Rs5SI for last 6 months = Rs 102×10×1100×2=Rs5.25So smount at the end of 1 year= Rs (100+5+5.25)=Rs110.25Rate = 110.25−100=10.25%

Let the sum be Rs 100 then
SI for first 6 months = Rs $\frac{100 \times 10 \times 1}{100 \times 2} = R s 5$
SI for last 6 months = Rs $\frac{102 \times 10 \times 1}{100 \times 2} = R s 5.25$
So smount at the end of 1 year
= Rs $(100 + 5 + 5.25) = R s 110.25$
Rate = $110.25 - 100 = 10.25$ %