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:

10%

10.25%

10.5%

None of these

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.$ \left(\dfrac{100 \times 10 \times 1}{100 \times 2} \right) $= Rs. 5

S.I. for last 6 months = Rs.$ \left(\dfrac{105 \times 10 \times 1}{100 \times 2} \right) $= Rs. 5.25

So, amount at the end of 1 year = Rs. $\left(100 + 5 + 5.25\right)$ = Rs. 110.25

$\therefore$ Effective rate = $\left(110.25 - 100\right)$ = 10.25%