Question

a sum of money, invested at compound interest amounts to ₹19360 in 2 years and to ₹23,425.60 in 4 years. Find the rate per cent and the original sum of money

Answer 1

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Answer 2

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Le the Sum of Money be Rs. x.
Let the rate of Interest be r%.

In First Case,
 
Principal(P) = Rs. x
Amount = Rs. 19360
Rate% =r%
Time(n) = 2 years.

Using the Formula,

     Amount = P[ 1 + r%/100]ⁿ
     19360 = x[1 + r%/100]²
     19360/x = [1 + r%/100]² ------------------------eq(i)

In Second Case,

 Principal(P) = Rs. x
  Rate% = r%
 Time(n) = 4 years.
Amount = Rs. 23425.60

Again Using the Formula,
 
         Amount = P[1 + r%/100]ⁿ
        23425.60 = x[1 + r%/100]⁴

From eq(i),

                 23425.60 = x[1 + r%/100]² × [19360/x]
    $\frac{23425.60}{19360}$ = [1 + r%/100]²
           ⇒  $\frac{121}{100}$ = [1 + r%/100]²
                     ⇒    (11/10)² = [1 + r%/100]²

  On Comparing,
                     $\frac{11}{10} = 1 + \frac{r}{100}$    
                      $\frac{11}{10} -1 = \frac{r}{100}$     
                     $\frac{11 -10}{10} = \frac{r}{100}$
                        $\frac{1}{10} = \frac{r}{100}$
                           ⇒  r = 10%

Thus, the rate % will be 10%.


For the Principal,

  Using eq(i),
    19360/x  =  [1 +r%/100]²
     19360/x = [1 + 10/100]²
    19360/x = (11/10)²
    $\frac{19360}{x} = \frac{121}{100}$
       x = 160 × 100
  ⇒  x = Rs. 16,000

Thus, the Principal or the original sum of money is Rs 16,000.


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Hope it helps.

Have a Marvelous Day.