Question

Raghav buys a shop for $Rs.1,20,000$. He pays half of the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs.5000$ each. If the rate of interest is $12\%$ and he pays with the installments the interest due on the unpaid amount, find the total cost of the shop.

Answer 1

Raghav pays half of Rs. $1,20,000$ i.e. Rs. $60,000$ in cash and the balance Rs. $60,000$ in $12$ annual installments of Rs. $5000$ each. With each installment he pays interest on the unpaid amount at the rate of $12$ per annum.
$\therefore$ Amount of first installment $=Rs.5000+$ Interest on unpaid amount of $Rs.60000$
$=Rs.5000+Rs.(\frac{12}{100}\times 60000)$

$=Rs.5000+Rs.7200=Rs.12200$
$\therefore$ Amount of second installment$=Rs.5000+$ Interest on unpaid amount of $Rs.55000$
$=Rs.5000+Rs.(\frac{12}{100}\times 55000)$

$=Rs.5000+Rs.6600$ $=Rs.11600$
$\therefore$ Amount of third installments $=5000+$ Interest on unpaid amount of $Rs.50000$
$=Rs.5000+Rs.(\frac{12}{100}\times 50000)$

$=Rs.5000+Rs.6000$ $=Rs.11000$

Clearly, the amount of various installments form an A.P. with first term $Rs.12200$ and common difference$-600$

$\therefore$ Total cost of the shop $=Rs.[60,000+$ Sum of $12$ installments $]$

$=Rs.[60,000+\frac{12}{2}\{2\times 12200+(12-1)\times (-600)\left\}\right]$

$=Rs.[60,000+6(24,400-6,600\left)\right]$

$=Rs.[60,000+1,06,800]$

$=Rs.1,66,800$