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.

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.

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.)

What is the original source of this question?

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Jamie Nelson
ManhattanGMAT Instructor