Questions & Answers

Question

Answers

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: Itâ€™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 donâ€™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: Itâ€™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 donâ€™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.

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