Question

If in two years time a principal of Rs 100 amounts to Rs 121, when the interest at the rate of r% is compounded annually, then find the value of r.

Answer 1

Hint: Here, we use the formula $A = P{(1 + \dfrac{r}{{100}})^n}$ to calculate the value of r, where A is the amount, P is the principal, r is the rate of interest per conversion period and n is the number of conversion periods.

Complete step-by-step answer:
Given: Let Rs 121 be the amount and Rs 100 be the principal. Also,2 is the number of conversion period.
Now in order to calculate the rate of interest(r), we will substitute the given values in the above formula. Thus, our formula becomes,
 $121 = 100{(1 + \dfrac{r}{{100}})^2}$
Now we will first solve the bracket as per the BEDMAS rule
$121 = 100{(\dfrac{{100 + r}}{{100}})^2}$
Now we will bring 100 which is the principal to the left hand side from the right hand side and after bringing it to the left hand side it will be divided by 121 as it was multiplied on the right hand side and the basic rule says when we transpose something from one side of equal to sign to another side then the multiplication sign changes to division sign. Therefore, our equation becomes
$\dfrac{{121}}{{100}} = {(\dfrac{{100 + r}}{{100}})^2}$
Now let’s convert left hand side in the square form
${(\dfrac{{11}}{{10}})^2} = {(\dfrac{{100 + r}}{{100}})^2}$
Now we will take square root on both side
$\dfrac{{11}}{{10}} = \dfrac{{100 + r}}{{100}}$
Now we will bring 100 from the denominator of RHS to the numerator of LHS
$\dfrac{{11 \times 100}}{{10}} = 100 + r$
Now we will expand 100 as 10 multiply by 10 on the LHS because the product of 10 & 10 is 100
$\dfrac{{11 \times 10 \times 10}}{{10}} = 100 + r$
Now we will eliminate 10 from the LHS and our equation will become,
$11 \times 10 = 100 + r$
Now we will find the product of 11 & 10
110 = 100 + r
Now we will transpose 100 from RHS to LHS and we will subtract it from 110 of RHS
110 – 100 = r
Now we will find the difference of 110 & 100 to calculate r
Therefore, r = 10
Hence, the value of r is $10\% $.

Note: Don’t misunderstand the value of Amount as the Principal amount. Follow BEDMAS(Brackets Exponents Divide Multiply Addition Subtract) rule to avoid calculation error.