# Find the compound interest on Rs.8,000 for the period of $1\dfrac{1}{2}$ years at the rate of interest 10% per annum, if the interest is compounded half yearly.

Answer

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Hint: First calculate the amount by making use of the formula and then calculate the compound interest.

Complete step-by-step answer:

Given that the principal=Rs.8,000

Time period=$1\dfrac{1}{2}$ years=$\dfrac{3}{2}$ years

But, it is given that the interest is compounded half yearly

So,

t=$\dfrac{3}{2} \times 2 = $ 3years

Rate of interest=10%

Make use of the formula of amount

$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$

$

A = 8000{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} \\

A = 8000{\left( {\dfrac{{110}}{{100}}} \right)^3} \\

A = 8000 \times {(1.1)^3} \\

A = 8000 \times 1.331 \\

A = Rs.10648 \\

$

So, the amount =Rs.10648

We know that the compound interest is calculated by

Compound Interest=Amount-Principal

Compound Interest=10648-8000

Compound Interest=Rs.2648

Note: Whenever we are solving these types of problems related to compound interest, it is always recommended to first find out the amount using the formula and from this calculate the compound interest and also note that in this problem the interest is compounded half yearly and not annually.

Complete step-by-step answer:

Given that the principal=Rs.8,000

Time period=$1\dfrac{1}{2}$ years=$\dfrac{3}{2}$ years

But, it is given that the interest is compounded half yearly

So,

t=$\dfrac{3}{2} \times 2 = $ 3years

Rate of interest=10%

Make use of the formula of amount

$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$

$

A = 8000{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} \\

A = 8000{\left( {\dfrac{{110}}{{100}}} \right)^3} \\

A = 8000 \times {(1.1)^3} \\

A = 8000 \times 1.331 \\

A = Rs.10648 \\

$

So, the amount =Rs.10648

We know that the compound interest is calculated by

Compound Interest=Amount-Principal

Compound Interest=10648-8000

Compound Interest=Rs.2648

Note: Whenever we are solving these types of problems related to compound interest, it is always recommended to first find out the amount using the formula and from this calculate the compound interest and also note that in this problem the interest is compounded half yearly and not annually.

Last updated date: 22nd Sep 2023

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