Question

2. A sum of money, invested at compound
interest, amounts to 19,360 in 2 years and
to * 23,425.60 in 4 years. Find the rate
percent and the original sum of money.
​

Answer 1

Answer:

Step-by-step explanation:

Here is your answer---

→→→→→→→→→→

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]

    = [1 + r%/100]²

          ⇒   = [1 + r%/100]²

                    ⇒    (11/10)² = [1 + r%/100]²

 On Comparing,

                         

                           

                     

                       

                          ⇒  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

   

      x = 160 × 100

 ⇒  x = Rs. 16,000

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

Answer 2

Answer:

original sum of money is 16,000