Loan = P = Rs 2,36,000

First Installment of repayments = a = Rs 2,000

Increment of loan repayments = d = Rs 200

Here we assume that there is no interest as per simple interest or compound interest.

Sum = 2, 36, 000 = 2000 + 2200 + 2400 + ....

= a + (a + d) + (a + 2d) + .. n terms + last installment

Sum of AP series = [ 2a + (n-1) d] n/2 = [ 4000 + 200(n-1) ] n/2

we have to find the maximum value of n such that

1900 n + 100 n² < 2,36,000

n² + 19 n - 2360 < 0

factorizing:

2360 = 59 * 4 * 10 => 59 - 40 = 19

(n + 59 ) (n - 40) < 0

so -59 < n < 40

We take the value of n as 39.

So sum of AP series : Rs [4, 000 + 200 * 38 ] * 39/2

= Rs 5, 800 * 39 = Rs 2,26,200

The last installment = Rs 2,36,000 - Rs 2,26,200 = Rs Rs 9,800