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

Step-by-step explanation:

Total loan is 36,000

if the repayment increases by 1000 every month with in 8 months the total loan will be cleared.

Total installments = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

= 1000 + 2000 +3000 + 4000 + 5000 + 6000 + 7000 + 8000 =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.

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