Question

Jaspal Singh repays his total loan of Rs 118000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, what amount will be paid by him in the ${30}^{th}$ instalment?

Answer 1

Total amount of loan $=1,18,000$

Since the amount of each installment increases by $Rs.100$ every month.

$\therefore$ installments paid are in AP.

Amount of first installment $a=Rs.1000$

Increase in amount of each installment $d=Rs.100$

Amount paid by jaspal singh in ${30}^{th}$ installment=$a_{30}$

Now, $a_{30}=a+29d=1000+29\times 100=Rs.3900$

Amount of loan still paid by jaspal after 30 installments= Total loan-amount paid in 30 installments

=$118000-\frac{30}{2}[2\times 1000+(30-1)\times 100]$

=$118000-30\left[2450\right]=118000-73500=Rs.44500$