Question related to Installments

[mahajanakhil1985]

What annual installment will discharge a loan of Rs. 3540, due after 5 years? The rate of interest is 9% per annum.

I could not understand the explanation of this question. So, if somebody here can explain it, it would be indeed very helpful.

[muzumdar.siddharth]

What is the answer to the question?

If the answer is 1026.6 then I can explain to you the logic behind it. Else I myself am wrong in understanding the question.

[mahajanakhil1985]

Answer is 600.
Here is the explanation:
1. The first installment has to be paid after 1 year. It means that if we pay Rs. 100 as installment, then it will remain with bank for remaining 4 years.
2. Second after 2 years. In this case, Rs. 100 will remain with bank for remaining 3 years.
3. Third after 3 years. In this case, Rs. 100 will remain with bank for remaining 2 years.
4. Fourth after 4 years. In this case, Rs. 100 will remain with bank for remaining 1 years.
5. Fifth after 5 years. In this case, Rs. 100 will remain with for bank for remaining 0 years.

It means that SI for 4+3+2+1+0= 10years on amount of Rs. 100 is (100*9*10)/100= Rs. 90.

Total Principal= 5*100= Rs. 500.

It means that a loan of 500+90= Rs. 590 can be discharged by an installment of Rs. 100
So, a loan of Rs. 3540 can be discharged by an installment of (100/590)*3540 = Rs 600.

(I just could not understand that why the bank will provide us interest when we are discharging a loan. That's why, I asked this question here.)

[jnelson0612]

What is the original source of this question?