Question

Kiran deposited Rs.200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 11 % per annum, find the amount she gets on maturity.

Answer 1

Hint: We will first note down all the data given to us and then write the formula for the Interest that we are required to find. We will then put in the given values and get the interest and add that to the principal amount and thus, we have our answer.

Complete step-by-step answer:
Let us first discuss the formula we are going to use in this solution.
The formula for interest will be given by: $P\times \left({\displaystyle \frac{n(n+1)}{2}}\right)\times {\displaystyle \frac{1}{12}}\times {\displaystyle \frac{r}{100}}$, where P is the principal amount we deposited in the start, n is the number of months and r is the rate of interest.
Now, we are already given that the Principal amount is Rs. 200 which is deposited every month for 36 months. So, P = Rs. 200 and n = 36. The rate of interest is given to be 11%. Hence, r = 11%.
Now, let us put in all these values in the formula. We will get:-
$Interest=200\times \left({\displaystyle \frac{36(36+1)}{2}}\right)\times {\displaystyle \frac{1}{12}}\times {\displaystyle \frac{11}{100}}$
On opening up the brackets on the RHS, we will get:-
$\Rightarrow Interest=200\times {\displaystyle \frac{36\times 37}{2}}\times {\displaystyle \frac{1}{12}}\times {\displaystyle \frac{11}{100}}$
On simplifying the values on RHS, we will get:-
$\Rightarrow Interest=200\times {\displaystyle \frac{36\times 37}{2}}\times {\displaystyle \frac{1}{12}}\times {\displaystyle \frac{11}{100}}$
$\Rightarrow Interest=Rs.1221$
We now have the interest she gets on her money she deposited.
We now need to add this interest to the amount she deposited to get the required answer.
The amount she deposited in 1 month = Rs. 200
Therefore, the amount she deposited in 36 months = $Rs.200\times 36=Rs.7200$.
So, she deposited RS. 7200 on which she got Rs. 1221 as the interest.
Hence, the total amount she received was: Rs. (7200 + 1221) that is Rs. 8421.

Hence, the required answer is Rs. 8421.

Note: The students might make the mistake of not adding the amount she deposited at the end of the answer but leave when they found the interest which will make their solution incomplete. So, always read the question carefully and answer what is required.
Let us briefly understand the difference between simple interest and compound interest by an example.
Suppose you deposit some money in a bank and get simple interest on it, you will basically get the interest on the money you deposited in the start only. Even if you deposit more, that does not Increase your interest or anything. That is the reason we prefer compound interest in which if we deposit more, our interest also increases.