Question

The compound interest on Rs. 5600 for $1\dfrac{1}{2}$ years at 10% per annum, compounded annually, is
A) Rs. 882.70
B) Rs. 873.50
C) Rs. 868
D) Rs. 840

Answer 1

Hint: We have to find out how much Rs. 5600 will amount to after two years if the rate of interest is given as 10% and interest is compounded annually. We will first find the amount after one year using the formula \[\dfrac{{{\text{PRT}}}}{{{\text{100}}}}\]. When we calculate the compound interest, the total amount after one year is the new principal amount for the second year. Then, calculate the interest in the next year. At last, subtract the total amount from the principal amount to find the compound interest in two years.

Complete step by step solution:
First determine the amount after one year when the principal amount is Rs. 5600, time is 2 years and interest is 10%.
Calculate the interest after one year using the formula, \[\dfrac{{PRT}}{{100}}\], where $P$ is the principal amount, $R$ is the rate of interest and $T$ is the time period.
\[\dfrac{{5600\left( 1 \right)\left( {10} \right)}}{{100}} = 560\]
Hence, the total amount is the sum of interest and principal amount.
Total amount after one year, 5600+560=6160
When we calculate the compound interest, the total amount after one year is the new principal amount for the second year.
Now, calculate the interest when the principal amount is Rs. 6,160, time is $\dfrac{1}{2}$ years and the rate of interest is 10%.
$\dfrac{{6160\left( {\dfrac{1}{2}} \right)\left( {10} \right)}}{{100}} = 308$
Hence, the total amount after $1\dfrac{1}{2}$ years on Rs. 5600 at the rate of interest 10% compounded annually is 6160+308=6468
Now, we will calculate the interest by subtracting the principal amount from the total amount.
$C.I. = A - P$, where C.I. stands for compound interest.
Therefore,
 $
  C.I. = 6468 - 5600 \\
  C.I. = 868 \\
$
Hence, option C is correct.

Note: Make sure the time period that is given in the question is in years, and if it is given in months then convert it into years. Whenever we are given to calculate the compound interest, we first calculate the total amount and then subtract the principal amount from it.