Question

. A loan of Rs 36000 , was to be paid back in monthly installments , the first being 1000. The next month 2000 . At this rate of payment how many months would it take To clear the debt . ( repayment increases by 1000 every month )

Answer 1

It would take 8 months to clear the debt.

Step-by-step explanation:

We are given that a loan of Rs 36000 was to be paid back in monthly installments. The first being 1000, the next month 2000.

Repayment increases by 1000 every month.

Amount of the loan to be paid = Rs 36,000

• The first monthly installment paid is = Rs 1000

So, the amount of loan left after paying the first installment = Rs 36,000 - Rs 1000 = Rs 35,000

• The second monthly installment paid is = Rs 2000

So, the amount of loan left after paying the second installment = Rs 35,000 - Rs 2000 = Rs 33,000

• The third monthly installment paid is = Rs 3000

So, the amount of loan left after paying the first installment = Rs 33,000 - Rs 3000 = Rs 30,000

• The fourth monthly installment paid is = Rs 4000

So, the amount of loan left after paying the first installment = Rs 30,000 - Rs 4000 = Rs 26,000

• The fifth monthly installment paid is = Rs 5000

So, the amount of loan left after paying the first installment = Rs 26,000 - Rs 5000 = Rs 21,000

• The sixth monthly installment paid is = Rs 6000

So, the amount of loan left after paying the sixth installment = Rs 21,000 - Rs 6000 = Rs 15,000

• The seventh monthly installment paid is = Rs 7000

So, the amount of loan left after paying the seventh installment = Rs 15,000 - Rs 7000 = Rs 8,000

• The eighth monthly installment paid is = Rs 8000

So, the amount of loan left after paying the eighth installment = Rs 8000 - Rs 8000 = Rs 0

Hence, this shows that it will take 8 months to clear the debt of Rs 36,000.

Answer 2

The number of months taken to clear the debt = 8

Step-by-step explanation:

Loan amount = 36000

let the number of installments be n

Then

According to the question

$1000+2000+3000+4000+........ +\text{n times} = 36000$

This is an AP whose first term is 1000 and common difference is 1000

Sum of n terms of an AP whose first term is a and common difference d is given by

$S_n=\frac{n}{2}[2a+(n-1)d$

Therefore, here the sum will be

$36000=\frac{n}{2}[2\times 1000+(n-1)\times 1000]$

$\implies 36000=\frac{1000n}{2}(2+n-1)$

$\implies 36=\frac{n(n+1)}{2}$

$\implies n^2+n=72$

$\implies n^2+n-72=0$

$\implies n^2+9n-8n-72=0$

$\implies n(n+9)-8(n+9)=0$

$\implies (n+9)(n-8)=0$

$\implies n=8, -9$

But n is a natural number

Therefore, n = 8

Thus, it will take 8 months to clear the debt

Hope this answer is helpful.

Know More:

Q: A man arranges to pay off a debt of RS. 3600 by 40 annual installments which form an A.P. When 30 of the installments are paid, he dies leaving one - third of thhe debt unpaid, find the value of the first installment.

Click Here: https://brainly.in/question/900369