Multiple choice

What annual installment will discharge a debt of Rs. 4910 due in 5 years, the rate of simple interest being 9% per annum?

  1. Rs. 832.20

  2. Rs. 1100

  3. Rs. 900

  4. Rs. 1050

  5. None of these
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A Correct answer
Explanation

Let x be the annual installment. The debt is discharged by the sum of the installments plus the interest on each. The first installment (paid at end of year 1) earns interest for 4 years, the second for 3, etc. Total = 5x + x * 0.09 * (4+3+2+1) = 5x + x * 0.09 * 10 = 5x + 0.9x = 5.9x. 5.9x = 4910. x = 4910 / 5.9 = 832.20.

AI explanation

The formula for the annual installment to clear a debt is 100 times the total debt divided by 100 plus the number of years times rate minus the number of years. Plugging in the values gives 100 times 4910 divided by 100 plus 5 times 9 minus 5. Simplifying the denominator gives 100 plus 45 minus 5, which is 140. Dividing 491000 by 140 gives the installment of Rs. 832.20.

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