An automobile financier claims to be lending money at simple interest,

1.	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 20%, the effective rate of interest becomes:1). 20%2). 20.25%3).4). 20.75%
Answer» Let the Principle VALUE be Rs. 100. Given, interest rate is 20% and is applied every six month. Formula used:Simple interest calculated annually$(,\;S.I = \FRAC{{P \times R \times T}}{{100}})$ For six MONTHS, T = ½ ∴Simple interest for first six month,$(\;S.{I_1} = \frac{{100 \times 20 \times \frac{1}{2}}}{{100}})$ = Rs. 10 New principle value = Rs. 110 ⇒Simple interst for next six month,$(\;S.{I_2} = \frac{{\left( {110 \times 20 \times \frac{1}{2}} \right)}}{{100}})$ = Rs. 11 Hence, TOTAL amount at the end of one year = Rs. 110 + 11 =Rs. 121 ⇒ Effective rate of interest$( = \frac{{121 - 100}}{{100}} \times 100)$ = 21%

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 20%, the effective rate of interest becomes:1). 20%2). 20.25%3).4). 20.75%

Answer»

Let the Principle VALUE be Rs. 100.

Given, interest rate is 20% and is applied every six month.

Formula used:Simple interest calculated annually$(,\;S.I = \FRAC{{P \times R \times T}}{{100}})$

For six MONTHS, T = ½

∴Simple interest for first six month,$(\;S.{I_1} = \frac{{100 \times 20 \times \frac{1}{2}}}{{100}})$

= Rs. 10

New principle value = Rs. 110

⇒Simple interst for next six month,$(\;S.{I_2} = \frac{{\left( {110 \times 20 \times \frac{1}{2}} \right)}}{{100}})$

= Rs. 11

Hence, TOTAL amount at the end of one year = Rs. 110 + 11

=Rs. 121

⇒ Effective rate of interest$( = \frac{{121 - 100}}{{100}} \times 100)$

= 21%