Question

3 Find the compound interest on 3000 of
the rate of 6% per annum for 3/2
compound half yearly​

Answer 1

Answer ::

The compound interest is Rs. 573.048.

Step-by-step explanation ::

To Find :-

• The compound interest

Solution :-

Given that,

• Principal ( P ) = Rs. 3000
• Rate ( R ) = 6%
• Time ( n ) = 3/2 years compounded half-yearly

As we know that,

Compound interest = Amount - Principal,

Therefore, first we need to find out the amount,

As we know that,

[ When Interest is compounded half-yearly ]

$\bf{Amount = \bigg\{P \times \bigg( 1 + \dfrac{R}{100} \bigg) ^{2n} \bigg \}}$

$\sf{A = \bigg\{P \times \bigg( 1 + \dfrac{R}{100} \bigg) ^{2 \times \frac{3}{2}} \bigg \}} \\ \\ \\ \sf{A = \bigg\{P \times \bigg( 1 + \dfrac{R}{100} \bigg) ^{ \cancel{2} \times \frac{3}{ \cancel{2}}} \bigg \}} \\ \\ \\ \sf{A = \bigg\{P \times \bigg( 1 + \dfrac{R}{100} \bigg) ^{3} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3000 \times \bigg( 1 + \dfrac{6}{100} \bigg) ^{3} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3000 \times \bigg( 1 + \cancel{\dfrac{6}{100}} \bigg) ^{3} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3000 \times \bigg( 1 + \dfrac{3}{50} \bigg) ^{3} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3000 \times \bigg( \dfrac{53}{50} \bigg) ^{3} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3000 \times \dfrac{53}{50} \times \dfrac{53}{50} \times \dfrac{53}{50} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3 \cancel{0} \cancel{0} \cancel{0} \times \dfrac{53}{5 \cancel{0}} \times \dfrac{53}{5 \cancel{0}} \times \dfrac{53}{5 \cancel{0}} \bigg \}} \\ \\ \\ \sf{A = \bigg\{3 \times \dfrac{53}{5} \times \dfrac{53}{5} \times \dfrac{53}{5} \bigg \}} \\ \\ \\ \sf{A = \dfrac{446631}{125}} \\ \\ \\ \sf{A =\cancel{\dfrac{446631}{125}}} \\ \\ \\ \sf{A = 3573.048}$

Now, Compound Interest is,

$\bf{Compound \: interest = Amount - Principal} \\ \\ \sf{ \longmapsto \: Rs. ( 3573.048 - 3000 )} \\ \\ \\ \frak{ \green{\longmapsto \: Rs. 573.048}}$

Hence, the compound interest is Rs. 573.048.