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
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Karanraj123:
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Hello Dear.
Here is your answer---
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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]
= [1 + r%/100]²
⇒
= [1 + r%/100]²
⇒ (11/10)² = [1 + r%/100]²
On Comparing,
![\frac{11 -10}{10} = \frac{r}{100} \frac{11 -10}{10} = \frac{r}{100}](https://tex.z-dn.net/?f=+%5Cfrac%7B11+-10%7D%7B10%7D+%3D++%5Cfrac%7Br%7D%7B100%7D+)
![\frac{1}{10} = \frac{r}{100} \frac{1}{10} = \frac{r}{100}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B10%7D+%3D+%5Cfrac%7Br%7D%7B100%7D+)
⇒ 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} \frac{19360}{x} = \frac{121}{100}](https://tex.z-dn.net/?f=+%5Cfrac%7B19360%7D%7Bx%7D+%3D+%5Cfrac%7B121%7D%7B100%7D)
x = 160 × 100
⇒ x = Rs. 16,000
Thus, the Principal or the original sum of money is Rs 16,000.
→→→→→→→→→→
Hope it helps.
Have a Marvelous Day.
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]
⇒
⇒ (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.
→→→→→→→→→→
Hope it helps.
Have a Marvelous Day.
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