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 is
A. \[Rs.8420\]
B. \[Rs.7920\]
C. \[Rs.7200\]
D. \[Rs.7000\]
Answer
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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.
Complete step-by-step answer:
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).
Note: It’s necessary to keep in mind that the compound interest is compounded annually and the total amount is to be paid in two instalments. If we don’t consider the fact that the amount is to be paid in two instalments, we will get a wrong answer. Compound interest is the interest (extra money) that one needs to pay on a sum of money that has been taken as a loan.
Complete step-by-step answer:
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).
Note: It’s necessary to keep in mind that the compound interest is compounded annually and the total amount is to be paid in two instalments. If we don’t consider the fact that the amount is to be paid in two instalments, we will get a wrong answer. Compound interest is the interest (extra money) that one needs to pay on a sum of money that has been taken as a loan.
Last updated date: 20th Sep 2023
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