A person has a recurring deposit account in a bank for $2$ years at $9\%$ per annum. If the person gets ₹ $7837.50$ at the time of maturity, find the monthly installment.
Let money deposited per month $= P =$ ₹ $100$
Number of months $= n = 24$ $\;\;\;$ [$2$ years]
Rate of interest $= r = 9 \%$
Interest $= I = P \times \dfrac{n \left(n + 1\right)}{12} \times \dfrac{r}{100}$
i.e. $\;$ $I =$ ₹ $\left(100 \times \dfrac{24 \times 25}{12} \times \dfrac{9}{100}\right) = $ ₹ $450$
Money deposited in $24$ months $= 24 \times $ ₹ $100 = $ ₹ $2400$
Maturity value (M.V) $= $ ₹ $\left(2400 + 450\right) = $ ₹ $2850$
When M.V is ₹ $2850$, monthly installment $= $ ₹ $100$
When M.V is ₹ $7837.50$, monthly installment $= $ ₹ $\dfrac{100 \times 7837.50}{2850} = $ ₹ $275$