Question

Saurabh opened a recurring deposit with a bank for $2\frac{1}{2}$ years. The bank paid Rs 4137.50 on maturity. If the rate of interest is 8% per annum, calculate the monthly instalment.?
[4 MARKS]

Answer 1

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

Given n = 2 $\frac{1}{2}$ years = 30 months, r = 8% p.a. and maturity value = Rs 4137.50.
Let the monthly instalment be Rs $x$
Then, money deposited in 30 months
= Rs($x\times 30$) = Rs 30 $x$
Equivalent principal for 1 month,
$P=x\left[\frac{n(n+1)}{2}\right]=Rs\left[\frac{(x\times 30\times 31)}{2}\right]=Rs465x.$
$\therefore Interest=P\times \frac{r}{100}\times \frac{1}{12}=Rs[465x\times \frac{8}{100}\times \frac{1}{12}]=Rs\frac{310x}{100}$
$\therefore$ Maturity value = Total money deposited + Interest
$\Rightarrow Rs4137.50=30x+\frac{310x}{100}=\left[\frac{3000x+310x}{100}\right]\Rightarrow Rs(4137.50\times 100)=3310x\Rightarrow 3310x=413750\Rightarrow x=\frac{413750}{3310}=125$
Hence, the monthly instalment is Rs 125.