Question

A house is sold for $Rs30,000$ cash or $Rs17,500$ cash down payment and instalments of $Rs1,600$ per month for eight months. Determine the approximate rate of interest for instalment.

• A. $6.5\%$
• B. $6.8\%$
• C. $6.2\%$
• D. None of these
• E. $6.3\%$

Answer 1

Answer: (A)

$6.5\%$

$\Rightarrow$ Cash price = $Rs.30,000$

$\Rightarrow$ Cash down payment = $Rs.17500$

$\Rightarrow$ Total amount paid in 8 monthly installments = $Rs.(1600\times 8)=Rs.12800$

$\Rightarrow$ Total amount paid under installment paln = $Rs.17500+Rs.12800=Rs.30300$

$\Rightarrow$ Interest charged = $Rs.30300-Rs.30000=Rs.300$

$\Rightarrow$ Principal for 1st month = $Rs.30000-Rs.17500=Rs.12500$

$\Rightarrow$ Principal for 2nd month = $Rs.12500-Rs.1600=Rs.10900$

$\Rightarrow$ Principal for 3rd month = $Rs.10900-Rs.1600=Rs.9300$

$\Rightarrow$ Principal for 4th month = $Rs.9300-Rs.1600=Rs.7700$

$\Rightarrow$ Principal for 5th month = $Rs.7700-Rs.1600=Rs.6100$

$\Rightarrow$ Principal for 6th month = $Rs.6100-Rs.1600=Rs.4500$

$\Rightarrow$ Principal for 7th month = $Rs.4500-Rs.1600=Rs.2900$

$\Rightarrow$ Principal for 8th month = $Rs.2900-Rs.1600=Rs.1300$

$\Rightarrow$ Total principal = $Rs.55200$

$\Rightarrow$ The last installment of Rs.1600 includes Rs.1300 plus Rs.300 interest.

$\Rightarrow$ Time = 1 month = $\frac{1}{12}$year, Interest = Rs.$300$

$\Rightarrow$ Interest = $\frac{P\times T\times R}{100}$

$\Rightarrow$ $R=\frac{I\times 100}{P\times T}$

$\Rightarrow$ $R=\frac{300\times 100}{55200\times \frac{1}{12}}=\frac{300\times 100\times 12}{55200}=\frac{150}{23}=6.5$

$\therefore$ $Rate=6.5\%$