Question

Mrs. Sen opens an account in a bank by depositing Rs.10000 and gets back Rs.12850 after 3 years. What was the rate of interest on it?

Answer 1

Hint:
Here, we will find the simple interest using the amount formula. Then we will substitute the obtained interest in the simple interest formula to find the rate of interest. Simple interest is defined as the interest calculated for the principal at a rate for a period of time.

Formula Used:
We will use the following formula:
1) Simple Interest is given by the formula \[S.I. = A - P\] where \[A\] is the amount and \[P\] is the principal.
2) Simple Interest is given by the formula \[S.I. = \dfrac{{P \times n \times r}}{{100}}\] where \[S.I\] is the Simple Interest, \[P\] is the principal, \[r\] is the rate of Interest and \[n\] is the number of years.

Complete step by step solution:
We are given that Mrs. Sen deposits Rs.10000 when opening a bank account and gets back Rs.12850 after 3 years with an interest.
Simple Interest can be calculated by subtracting principal from the amount.
Substituting amount \[A = Rs.12850\] and the principal \[P = Rs.10000\] in the formula \[S.I. = A - P\], we get
\[S.I. = 12850 - 10000\]
By subtracting the numbers, we get
\[ \Rightarrow S.I. = {\rm{Rs}}.2850\]
Now substituting \[P = 10000,n = 3years\] and \[S.I. = {\rm{Rs}}.2850\] in the formula\[S.I. = \dfrac{{P \times n \times r}}{{100}}\], we get
\[2850 = \dfrac{{10000 \times 3 \times R}}{{100}}\]
By cross multiplying the term, we get
\[ \Rightarrow R = \dfrac{{2850 \times 100}}{{10000 \times 3}}\]
Simplifying the expression
\[ \Rightarrow R = \dfrac{{285}}{{30}}\]
Dividing 285 by 30, we get
\[ \Rightarrow R = 9.5\% \]

Therefore, the rate of interest is \[9.5\% \].

Note:
We should not get confused between simple interest and compound interest. The main difference between simple interest and compound interest is that simple interest is based only on the principal amount whereas compound interest is based on the principal amount and also the interest compounded for a period. Whenever opening a bank account, the interest will be simple interest. Thus we will use the simple interest formula.