Question : A computer is available for INR 39,000 on cash payment or INR 19,000 as cash payment followed by five monthly instalments of INR 4,200 each. What is the rate of interest per annum under the instalment plan?
Option 1: $20 \frac{19}{29} \%$
Option 2: $20 \frac{17}{29} \%$
Option 3: $20 \frac{20}{29} \%$
Option 4: $20 \frac{18}{29} \%$
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Correct Answer: $20 \frac{20}{29} \%$
Solution :
Total cost of the computer = Rs. 39000
Down payment = Rs. 19000
Balance = Rs. 20000
Let the rate of interest be $r$
Here simple interest is denoted by S.I.
Hence, the amount of Rs. 20000 for 5 months
= $20000+ \frac{20000\times r\times \frac{5}{12}}{100}$
= $20000+ \frac{250r}{3}$
The customer pays the shopkeeper Rs. 4200 after 1 month, Rs. 4200 after 2 months, ...... and Rs. 4200 after 5 months.
Thus, the shopkeeper keeps Rs. 4200 for 4 months, Rs. 4200 for 3 months, Rs. 4200 for 2 months, Rs. 4200 for 1 month and Rs. 4200 at the end.
The sum of the amounts of these instalments
= (Rs. 4200 + S.I. on Rs 4200 for 4 months) + (Rs. 4200 + S.I. on Rs. 4200 for 3 months) + ...... + (Rs. 4200 + S.I. on Rs. 4200 for 1 month) + Rs. 4200
= Rs. (4200 × 5) + S.I. on Rs. 4200 for (4 + 3 + 2 + 1) months
= Rs. 21000 + S.I. on Rs. 4200 for 10 months
= $21000+4200\times r\times \frac{10}{12}\times \frac{1}{100}=21000+35r$
Hence, $20000+ \frac{250r}{3}=21000+35r$
$⇒\frac{145r}{3}=1000$
$⇒r=\frac{600}{29}$
$⇒r=20\frac{20}{29}\%$
Hence, the correct answer is $20\frac{20}{29}\%$.
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