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Illustrations · Illustration 8

Q.John Ibrahim, a partner in Modern Tours and Travels withdrew money during the year ending March 31, 2020 from his capital account, for his personal use. Calculate interest on drawings in each of the following alternative situations, if rate of interest is 9 per cent per annum.

(a) If he withdrew ₹3,000 per month at the beginning of the month.
(b) If an amount of ₹3,000 per month was withdrawn by him at the end of each month.
(c) If the amounts withdrawn were: ₹12,000 on June 01, 2019, ₹8,000 on August 31, 2019, ₹3,000 on September 30, 2019, ₹7,000 on November 30, 2019, and ₹6,000 on January 31, 2020.
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A fixed monthly amount uses the average-period shortcut (6½ months at the start of the month, 5½ at the end); varying amounts on irregular dates need the product method, multiplying each withdrawal by the months it stayed out. All three parts of this problem are grounded in those two techniques.

Concept

For a fixed amount withdrawn at regular monthly intervals, the average period saves computing interest withdrawal-by-withdrawal: if withdrawn on the 1st of every month, the first withdrawal is outstanding 12 months and the last only 1 month, averaging (12+1)/2 = 6½ months; if withdrawn on the last day of every month, the first is outstanding 11 months and the last 0 months, averaging (11+0)/2 = 5½ months.

For varying amounts on irregular dates, use the product method: multiply each withdrawal by the number of months it remained outstanding (from the withdrawal date to the year-end), sum the products, then apply the rate for 1/12 of a year.

Solution — (a) ₹3,000 per month, beginning of each month

Average period = (12 + 1)/2 = 6½ months. Total drawings = ₹3,000 × 12 = ₹36,000.

Interest = ₹36,000 × 9/100 × 13/2 × 1/12 = ₹1,755.

Solution — (b) ₹3,000 per month, end of each month

Average period = (11 + 0)/2 = 5½ months.

Interest = ₹36,000 × 9/100 × 11/2 × 1/12 = ₹1,485.

Solution — (c) Varying amounts on different dates (product method)

DateAmount (₹)Time outstanding (months, to Mar 31, 2020)Product (₹)
June 1, 201912,000101,20,000
August 31, 20198,000756,000
September 30, 20193,000618,000
November 30, 20197,000428,000
January 31, 20206,000212,000
Total of products2,34,000

Interest = Total of products × Rate × 1/12 = ₹2,34,000 × 9/100 × 1/12 = ₹1,755.

✓Final answer

  1. ₹1,755 (average period 6½ months).
  2. ₹1,485 (average period 5½ months).
  3. ₹1,755 (product method, total products ₹2,34,000).

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