Kishore purchases a track suit for Rs.2400 cash or for Rs.1000 cash down…

Concept: In a cash-down-plus-installment purchase, the amount still owed after the down payment is a debt carrying simple interest at rate r% per annum. To find r, equate the future value of this debt (carried forward with interest to the date of the LAST installment) to the future value of the stream of installments (each earlier installment also carried forward with interest to that same date).

Application:

1. Principal still owed after the down payment = Rs.2400 - Rs.1000 = Rs.1400. This amount is outstanding for the 2 months until the last installment.

2. Future value of the outstanding principal at the end of 2 months, at rate r% per annum = 1400 + (1400 × r × 2)/(100 × 12).

3. The second installment of Rs.800 is paid exactly at the 2-month settlement point, so it contributes Rs.800 with no further interest. The first installment of Rs.800, paid at the end of month 1, must be carried forward one more month to the settlement point, becoming 800 + (800 × r × 1)/(100 × 12).

4. Future value of the installment stream at the settlement point = 800 + [800 + (800 × r × 1)/(100 × 12)] = 1600 + 800r/1200.

5. Equate the two future values: 1400 + 2800r/1200 = 1600 + 800r/1200.

6. Solve: 2000r/1200 = 200, giving r = 120.

Cross-check: Substituting r = 120 back: the principal side gives 1400 + (1400×120×2)/1200 = 1400 + 280 = 1680. The installment side gives 1600 + (800×120)/1200 = 1600 + 80 = 1680. Both sides match, confirming r = 120% per annum.

Result: The rate of interest is 120% per annum.