Question : If the amounts received at the end of the 2nd and 3rd year at compound Interest on a certain principal are Rs. 24,200 and Rs. 26,620, respectively, what is the rate of interest per annum?
Option 1: 10%
Option 2: 5%
Option 3: 20%
Option 4: 16%
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Correct Answer: 10%
Solution :
Given:
The amount received at the end of 2nd year at compound Interest on a certain principal = Rs. 24,200
The amount received at the end of 3rd year at compound Interest on a certain principal = Rs. 26,620
Formula used:
Amount = $P(1+\frac{R}{100})^{n}$ where n is the number of years.
Calculation:
Amount received at the end of 2nd year at compound Interest $= 24,200 =P(1+\frac{R}{100})^{2}$ ...(i)
Amount received at the end of 3rd year at compound Interest $= 26,620 =P(1+\frac{R}{100})^{3}$ ...(ii)
On dividing equation (i) by (ii) we get
$\frac{26620}{24200} = 1+\frac{R}{100}$
$\frac{11}{10} = 1+\frac{R}{100}$
$\frac{11}{10} -1 = \frac{R}{100}$
$\frac{1}{10} = \frac{R}{100}$
$R=10$%
Hence, the correct answer is 10%.
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