Question

Sanjay has a Recurring Deposit Account in a bank of Rs 2,000 per month at the rate of 10% per annum. At the time of maturity, he receives Rs 83,100. Find the time for which account was held.
[3 MARKS]

Answer 1

Formula: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

Let number of instalments be Rs x
Monthly instalment = Rs 2000
Equivalent principal for 1 month = Monthly instalment $\times \frac{n(n+1)}{2}=Rs2000\times \frac{x(x+1)}{2}$
$Interest=\frac{P\times R\times T}{100}=Rs2000\times \frac{x(x+1)}{2}\times \frac{10}{100}\times \frac{1}{12}$
Amount received on maturity = Rs 83,100
$\Rightarrow$ Total amount deposited + Interest = Rs 83,100
$\Rightarrow$ $2000x+2000\times \frac{x(x+1)}{2}\times \frac{10}{100}\times \frac{1}{12}=83,100$
$\Rightarrow 2000x+\frac{25}{3}x(x+1)=83,100$
$\Rightarrow \frac{6000x+25x(x+1)}{3}=83100$
$\Rightarrow 25(240x+x^2+x)=249300$
$\Rightarrow (x-36)(x+277)=0$
$\Rightarrow x=36andx=-277$ (neglectig - 277 because x cannot be negative)
$\therefore$ The time for which account was held = 36 months or 3 years