A person deposits a certain sum of money each month in a recurring deposit account of a bank. If the rate of interest is $8 \%$ per annum and the person gets ₹ $8088$ from the bank after $3$ years, find the value of the monthly installment.
Let money deposited per month $= P = $ ₹ $x$
Time for which money is deposited $= n = 3$ years $= 36$ months
Rate of interest $= r = 8\%$ per annum
Interest $= I = P \times \dfrac{n \left(n + 1\right)}{2 \times 12} \times \dfrac{r}{100}$
i.e. $\;$ $I =$ ₹ $\left[\dfrac{x \times 36 \times 37}{2 \times 12} \times \dfrac{8}{100}\right]$
i.e. $\;$ $I =$ ₹ $\left[\dfrac{111 x}{25}\right] = $ ₹ $4.44 x$
Total money deposited in $36$ months $= $ ₹ $36 x$
Maturity value (MV) $=$ Total money deposited $+ $ Interest
i.e. $\;$ $MV = $ ₹ $\left(36 x + 4.44 x\right) = $ ₹ $40.44 x$
Given: $\;$ $MV =$ ₹ $8088$
$\implies$ $40.44x = 8088$ $\implies$ $x = 200$
i.e. $\;$ money deposited per month $= $ ₹ $200$