Question

Mr. Sonu has a recurring deposit account and deposits Rs. 750 per month for 2 years. If he gets Rs. 19125 at the time of maturity, find the interest.

Answer 1

Hint: First, we will use the formula of market value, \[{\text{M.V.}} = {\text{P}} \times {\text{T}} + {\text{P}} \times \dfrac{{{\text{T}}\left( {{\text{T + 1}}} \right)}}{{100}} \times \dfrac{{\text{R}}}{{100}}\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{R}}\] is the interest rate per year and \[{\text{T}}\] is the time the money is invested in years. Apply this formula, and then use the given values to find the required value.

Complete step by step answer:

We are given that Sonu has a recurring deposit account and deposits Rs. 750 per month for 2 years.
Let us assume that \[r\] represents the interest.
Converting the time 2 years in months by multiplying it with 12, we get
\[
   \Rightarrow 2 \times 12 \\
   \Rightarrow 24{\text{ months}} \\
 \]
We know that the formula of market value, \[{\text{M.V.}} = {\text{P}} \times {\text{T}} + {\text{P}} \times \dfrac{{{\text{T}}\left( {{\text{T + 1}}} \right)}}{{100}} \times \dfrac{{\text{R}}}{{100}}\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{R}}\] is the interest rate per year and \[{\text{T}}\] is the time the money is invested in months.
First, we have to find the values of M.V. , \[{\text{P}}\] and \[{\text{T}}\]for the simple interest.
\[{\text{M.V.}} = 19125\]
\[{\text{P}} = 750\]
\[{\text{T}} = 24\]
We will now substitute the above values to compute the rate of interest using the above formula.
\[
   \Rightarrow 19125 = 750 \times 24 + 750 \times \dfrac{{24\left( {24 + 1} \right)}}{{100}} \times \dfrac{{\text{R}}}{{100}} \\
   \Rightarrow 19125 = 18000 + \dfrac{{18750{\text{R}}}}{{100}} \\
 \]
Subtracting the above equation by \[18000\] on both sides, we get
\[
   \Rightarrow 19125 - 18000 = 18000 + \dfrac{{18750{\text{R}}}}{{100}} - 18000 \\
   \Rightarrow 1125 = \dfrac{{18750{\text{R}}}}{{100}} \\
 \]

Multiplying the above equation by \[\dfrac{{100}}{{18750}}\] on both sides, we get
\[
   \Rightarrow \dfrac{{100}}{{18750}}\left( {1125} \right) = \dfrac{{100}}{{18750}} \times \dfrac{{18750{\text{R}}}}{{100}} \\
   \Rightarrow \dfrac{{112500}}{{18750}} = {\text{R}} \\
   \Rightarrow {\text{R}} = 6\% \\
 \]
Thus, the interest Is 6%.

Note: In solving these types of questions, the possibility of mistake can be not using the appropriate formula. One should remember that market value is computed only on the months instead of years. Students may solve the question by using the formula for amount is \[{\text{P}}\left( {1 + \dfrac{{{\text{RT}}}}{{100}}} \right)\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{R}}\] is the interest rate per year and \[{\text{T}}\] is the time the money is invested in years, which is wrong. By substituting the values in the above-mentioned formula, we can compute the time. DO not forget to convert time in months or else the answer will be wrong.