Multiple choice

A sum of Rs. 8,400 is taken as a loan. This is to be paid in two equal installments. If the rate of interest is 10% per annum, compounded annually, then the value of each installment is

  1. Rs. 4,200

  2. Rs. 4,480

  3. Rs. 4,840

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let installment be X. Loan = X/(1.1) + X/(1.1)^2 = 8400. X(1/1.1 + 1/1.21) = 8400. X(1.1 + 1)/1.21 = 8400. X(2.1/1.21) = 8400. X = 8400 * 1.21 / 2.1 = 4000 * 1.21 = 4840.

AI explanation

Let the value of each installment be x. For a two-year loan, the present value formula gives 8400 equals x divided by 1.1 plus x divided by 1.21. Finding a common denominator results in 8400 equals 1.1x plus x, all divided by 1.21, which simplifies to 10164 equals 2.1x. Dividing 10164 by 2.1 gives the value of each installment as Rs. 4,840. The value of each installment is Rs. 4,840.

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