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Question

# Mrs. Sarojini deposits Rs1600 per month in a Cumulative or Recurring Deposit Account at 9% p.a. simple interest. If she gets Rs 65,592 at the time of maturity, find the total time for which account was held? [4 MARKS]

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Solution

## Formula: 1 Mark Steps: 2 Marks Answer: 1 Mark Monthly instalment = Rs 1600 Let the required time be x months Total amount deposited = Rs 160 x Principal for 1 month = Monthly instalment ×n(n+1)2 Rs 1600×x(x+1)2 Interest=P×R×T100 =1600×x(x+1)2×9100×112 =16x(x+1)×32×4=6x(x+1) According to question, Amount received on maturity = Rs 65592 ⇒ Total amount deposited + Interest = 65592 ⇒1600x+6x(x+1)=65592 ⇒1600x+6x2+6x=65592 ⇒6x2+1606x−65592=0 ⇒3x2+803x−32796=0 ⇒3x2+911x−108x−32796=0 ⇒3x2+911x−108x−32796=0 ⇒x(3x+911)−36(3x+911)=0 ⇒(3x+911)(x−36)=0 ⇒3x+911=0 or x−36=0 ⇒x=−9113 (Rejected) or x = 36 ∴ Total time for which account was held = 36 months =3612=3 years

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