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# Find the compound interest on Rs. 20,000 for 2 years, compounded annually at 10% per annum.A) 4200B) 4300C) 4400D) 4500  Hint: First calculate the final amount needed to pay after two year then subtract this final amount to the given principal amount to calculate the compound interest in two years.

Given principal amount is
P=Rs 20000
Time to repay the amount is
T= 2 years
Rate of interest is
R=10% per annum
To find the amount of compound interest after 2 years
C.I. = ?
To calculate the compound interest first we will calculate the final amount that we need to pay after 2 year
We know that the formula to calculate the final amount
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
On putting the given values
$A = 20000 \times {\left( {1 + \dfrac{{10}}{{100}}} \right)^2}$
On simplification

$A = 20000 \times \dfrac{{121}}{{100}}$
Now we will calculate the compound interest
We know that

∴ $C.I. = A - P$
On putting the values of A and P
We get
$= Rs.24,200 - Rs.20,000$
On subtracting
We get
$= Rs.4200.$

Hence the compound interest that I need to pay after two year will be equal to Rs 4200.
Therefore the correct option is ‘A’

Additional information: When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.

Note: The interest rate for the first year in compound interest is the same as that in case of simple interest, Other than the first year, the interest compounded annually is always greater than that in case of simple interest.
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