Question

The bank offers interest at rate 7% p.a. compounded yearly. What interest will be received at the end of 5 years if Rs. 10,000 are deposited. Calculate by the method of compound interest.
A.4025
B.4025.5
C.4035
D.3025

Answer 1

Hint: Here we are given the principal amount of money, the rate of interest and it is to be compounded annually for 5 years. We will find out the compound interest using the formula. Consider all values given in question and try to identify which one to use where.
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
This will help in understanding the problem.

Complete step-by-step answer:
Here, we have the principal amount given (P) = 10,000Rs.
The rate of interest given by bank per annum (r) = 7%
The total duration given is 5 years.
As we know, the formula of compound interest is
 \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
A is the total amount. R is rate of interest and P is the principal amount
Compounded for two years.
Given in the question, $ P = 10,000Rs,r = 7\% ,n = 5years $
\[
  A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} \\
   \Rightarrow A = 10000{\left( {1 + \dfrac{7}{{100}}} \right)^5} \;
 \]
Going further by adding the fraction
\[
   \Rightarrow A = 10000{\left( {\dfrac{{107}}{{100}}} \right)^5} \\
   \Rightarrow A = 10000{(1.07)^5} \;
 \]
After calculating the exponent, we get
\[
   \Rightarrow A = 10000(1.40255) \\
   \Rightarrow A = 14025.5Rs. \;
 \]
So, the amount after two years will be
 \[A = 14025.5Rs.\]
The compound interest will be
 $
  Interest = Amount - Principal \\
   \Rightarrow Interest = 14025.5 - 10000 \\
   \Rightarrow Interest = 4025.5Rs. \;
  $
Hence, option (b) is the correct option.
So, the correct answer is “Option B”.

Note: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.