Question

Dinesh has a Recurring Deposit Account in a bank for $3\frac{1}{2}$ years at $9\frac{1}{2}\%p.a.$ If he gets Rs 78,638 at the time of maturity, find the monthly instalment.
[4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Suppose the monthly instalment = Rs $x$
$Time=3\frac{1}{2}years=\frac{7}{2}\times 12months=42months$
Total amount deposited = $Rs42\times x=Rs42x$
Principal for 1 month = Monthly instalment $\times \frac{n(n+1)}{2}$
$=Rsx\times \frac{42(42+1)}{3}$
$=Rs21x\times 43$
= Rs 903 $x$
$Interest=\frac{P\times R\times T}{100}$
$=Rs\frac{903x\times 19\times 1}{100\times 12\times 2}=Rs\frac{5719x}{800}$
According to question,
Amount received on maturity = 78638
$\Rightarrow$ Total money deposited + Interest = 78638
$\Rightarrow 42x+\frac{5719}{800}x=78638$
$\Rightarrow \frac{33600x+5719x}{800}=78638$
$\Rightarrow 39319x=78638\times 800$
$\Rightarrow x=\frac{78638\times 800}{39319}$
$\Rightarrow x=Rs1600$
$\therefore$ Monthly istalment = Rs 1600