Question

Amit deposited 150 per month in a bank for 8 months under the recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8 % per annum and the interest is calculated at the end of every month?

Answer 1

Hint: To solve this question, we will first analyze the principal P is Rs. 150 and r = 8 and the number of months, n = 8. We have the formula to calculate SI (Simple Interest) given below.
\[SI=P\times \dfrac{n\left( n+1 \right)}{2\times 12}\times \dfrac{r}{100}\]
Then finally, we will calculate the amount or the maturity value by \[MV=SI+150\times 8.\]

Complete step-by-step solution:
We are given that Amit deposits Rs. 150 per month. The duration for which he does this is 8 months and it is a recurring deposit scheme.
The Principal, i.e. the installment per month is Rs. 150
\[\Rightarrow P=Rs.150\]
The number of months is 8.
\[\Rightarrow n=8\]
Also, the rate of interest is given to be 8 %.
\[\Rightarrow r=8%\]
There is a formula to calculate the simple interest when n is the number of months and r is the rate. It is given as,
\[SI=P\times \dfrac{n\left( n+1 \right)}{2\times 12}\times \dfrac{r}{100}\]
Here, 12 is divided in this formula as there are 12 months in a year and we are considering monthly payment. Substituting the value of P = Rs. 150, r = 8 and n = 8, we have,
\[\Rightarrow SI=150\times \dfrac{8\left( 8+1 \right)}{2\times 12}\times \dfrac{8}{100}\]
\[\Rightarrow SI=150\times \dfrac{4\left( 9 \right)}{12}\times \dfrac{8}{100}\]
\[\Rightarrow SI=150\times 3\times 0.08\]
\[\Rightarrow SI=36\]
So, we have a simple interest as Rs. 36.
Now, finally, we will calculate the maturity value by adding SI to 150 of 8 months.
Rs. 150 for 8 months is \[150\times 8=1200.\]
So, the maturity value will be
\[\Rightarrow 1200+SI\]
\[\Rightarrow 1200+36\]
\[\Rightarrow 1236\]
Therefore, the maturity value Amit will have at the end of 8 months is Rs. 1236.

Note: Another method to solve this question can be calculating the amount of each month separately and then adding all the monthly received amounts to get the maturity value. This method although is long and involves a lot of calculation mistakes. Instead, the above formula is easy to use.