Question

How much more does a man get by investing 40000 at 40% p.a. compound interest , compounded yearly, than at 40% p.a. compound interest, compounded yearly per one year?
A) 1000
B) 1200
C) 1500
D) 1600

Answer 1

Hint:
To calculate the amount we need the value of principal amount, rate of interest and the year which is given in the question. Then we will use the formula of amount by putting all the values of amount, rate of interest and the year.
 Formula used: $A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$
Where A is the amount, P is the principal amount and R is the rate of interest.

Complete step by step solution:
First we will calculate the amount when the interest is compounded yearly,
Formula for amount is
$A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}$

Where A is the amount, P is the principal amount and R is the rate of interest.
Now, putting the values in the question.
$
   P=40000 \\
  R=40%p.a. \\
  n=1 \\
$
We get the amount $A=40000{{\left( 1+\dfrac{40}{100} \right)}^{1}}$
Further simplifying it, we get
$\Rightarrow A=40000{{\left( 1+\dfrac{40}{100} \right)}^{1}}$
Now, diving 40 by 100 in the bracket.
$\Rightarrow A=40000{{\left( 1+0.4 \right)}^{1}}$
Now adding terms inside the brackets, we get
$\Rightarrow A=40000\times 1.4$
We will multiply the terms now.
$\Rightarrow A=56000$
Again we will calculate the amount when the interest is compounded half yearly,
Formula for amount is
$A=P{{\left( 1+\dfrac{R}{2\times 100} \right)}^{n\times 2}}$

Where A is the amount, P is the principal amount and R is the rate of interest.
Now, putting the values in the question.
$
   P=40000 \\
  R=40%p.a. \\
  n=1 \\
$
We get the amount $A=40000{{\left( 1+\dfrac{40}{2\times 100} \right)}^{2}}$
Further simplifying it, we get
$\Rightarrow A=40000{{\left( 1+\dfrac{40}{2\times 100} \right)}^{2}}$
Now, diving 40 by 100 in the bracket.
$\Rightarrow A=40000{{\left( 1+0.2 \right)}^{2}}$
Now adding terms inside the brackets, we get
$\Rightarrow A=40000\times {{0.2}^{2}}$
now, calculating square of 0.2
$\Rightarrow A=40000\times 0.04$
We will multiply the terms now.
So the difference of the amount
$
\Rightarrow Rs\,57600-Rs\,56000 \\
\Rightarrow Rs\,1600 \\
$

Note:
we need to know one more term which is compound interest and it is defined as the sum of the interest and the principal sum of a loan and also it is defined as the frequency at which our interest is calculated yearly or annually.