Question

# A sum of $Rs.11000$ was taken as a loan. This is to be repaid in two equal instalments. If the rate of interest be $20%$ compounded annually, then the value of each instalment isA. $Rs.8420$B. $Rs.7920$C. $Rs.7200$D. $Rs.7000$

Hint: Use the formula to calculate the compound interest (compounded annually) $P=\dfrac{x}{{{\left( 1+\dfrac{R}{100} \right)}^{T}}}+\dfrac{x}{{{\left( 1+\dfrac{R}{100} \right)}^{2T}}}$ where $x$ is the amount to be paid in each instalment, $P$ is the principal money on which interest is added, $R$ is the rate of interest and $T$ is the time after which amount will be paid back.

We have a sum of $Rs.11000$ which is to be repaid after adding a compound interest at a rate of $20%$ compounded annually. As the interest is to be compounded annually, we have $T=1$ year.
To calculate the amount to be paid in each instalment, we will use the formula $P=\dfrac{x}{{{\left( 1+\dfrac{R}{100} \right)}^{T}}}+\dfrac{x}{{{\left( 1+\dfrac{R}{100} \right)}^{2T}}}$ where $x$ is the amount to be paid after the interest is added, $P$ is the principal money on which interest is added, $R$ is the rate of interest and $T$ is the time after which amount will be paid back.
We have $P=Rs.11000,R=20%,T=1$ year. Substituting these values in the above formula, we have $11000=\dfrac{x}{\left( 1+\dfrac{20}{100} \right)}+\dfrac{x}{{{\left( 1+\dfrac{20}{100} \right)}^{2}}}$.
Solving the above equation, we have $11000=\dfrac{5x}{6}+\dfrac{25x}{36}$.
Further simplifying the equation, we have $11000=\dfrac{55x}{36}$.
Thus, we have $x=\dfrac{11000\times 36}{55}=7200$.
Hence, the amount of each instalment is $Rs.7,200$, which is option (c).