Question

Find the compound interest on an amount of Rs 35000 for ​ \[ = 1\dfrac{1}{2}\] years compound semi-annually at the rate of 12% p.a.

Answer 1

Hint: Here we need to use the expression for the amount interest of principle , rate of interest and time then we can get the value of compound interest by the expression of compound interest where are are taking difference of amount and principle
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]
Where A is amount , P is principle, R rate of interest and n is the time,

Complete step-by-step answer:
We have principle (P)=35000
And rate of interest(R) =12%
And here compounded semi-annually it means time will be multiplied with two so ,
Time(n)= \[ = \dfrac{3}{2} \times 2year = 3year\]
And rate will be divided by 2 ie;
\[R = \dfrac{{12}}{2} = 6\% \]
So find the compound interest we can use formula for the amount here and we have the formula ,
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]
Substituting the value of n,R and p we get,
\[A = 35000{\left( {1 + \dfrac{6}{{100}}} \right)^3}\]
Solving the bracket first we get,
\[A = 35000{\left( {\dfrac{{100 + 6}}{{100}}} \right)^3}\]
\[ \Rightarrow A = 35000{\left( {\dfrac{{106}}{{100}}} \right)^3}\]
\[ \Rightarrow A = 35000{\left( {\dfrac{{53}}{{50}}} \right)^3}\]
As the power is three so we can write,
\[A = 35000\left( {\dfrac{{53}}{{50}} \times \dfrac{{53}}{{50}} \times \dfrac{{53}}{{50}}} \right)\]
After equating with principle value we get,
\[ \Rightarrow A = \dfrac{{7 \times 53 \times 53 \times 53}}{{5 \times 5}}\]
\[\
  \Rightarrow A = \dfrac{{7 \times 53 \times 53 \times 53}}{{5 \times 5}} \\
   \Rightarrow A = \dfrac{{1042139}}{{25}} \\
\ \]
So amount will be
\[A = 41685.56\]
Now to find find compound interest we need to subtract principle from amount so,
 Compound interest = amount – principal
\[C.I = A - P\]
Substituting the value of principal and amount we get,
$C.I = 41685.56 - 35000$
$\therefore C.I = 6685.56$

The compound interest is 6685.56

Note: Compound interest is an interest rate that is calculated on the principal and the interest accumulated over the previous period and compound interest is different from the simple interest where interest is not added to the principal while calculating the interest during the next period.