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]

Answer 1

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 $\times \frac{n(n+1)}{2}$
$Rs1600\times \frac{x(x+1)}{2}$
$Interest=\frac{P\times R\times T}{100}$
$=1600\times \frac{x(x+1)}{2}\times \frac{9}{100}\times \frac{1}{12}$
$=\frac{16x(x+1)\times 3}{2\times 4}=6x(x+1)$
According to question,
Amount received on maturity = Rs 65592
$\Rightarrow$ Total amount deposited + Interest = 65592
$\Rightarrow 1600x+6x(x+1)=65592$
$\Rightarrow 1600x+6x^2+6x=65592$
$\Rightarrow 6x^2+1606x-65592=0$
$\Rightarrow 3x^2+803x-32796=0$
$\Rightarrow 3x^2+911x-108x-32796=0$
$\Rightarrow 3x^2+911x-108x-32796=0$
$\Rightarrow x(3x+911)-36(3x+911)=0$
$\Rightarrow (3x+911)(x-36)=0$
$\Rightarrow 3x+911=0orx-36=0$
$\Rightarrow x=-\frac{911}{3}$ (Rejected) or $x$ = 36
$\therefore$ Total time for which account was held = 36 months
$=\frac{36}{12}=3years$