Question

Calculate the amount and the compound interest with out using direct formula on:

(1) Rs 4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.

(2) 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.

Note :
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Answer 1

$\Large{\boxed {\text \blue {Question: }}}$

Calculate the amount and the compound interest with out using direct formula on:

• Rs 4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.

• 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.

$\Large{ \boxed{\text \blue {To find: }}}$

In both parts we have to find :

• Amount
• Compound interest

$\Large{ \boxed{ \text{ \blue{Answer:}}}}$

$\Large{\orange{ \bold{Part \: 1: }}}$

year 1:

Here:

• P=₹4600
• R=10%
• T=1 year

Interest for 1 year:

$\tt{ Simple \: Interest = \dfrac{P \times R \times T}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{4600 \times 1 \times 10}{100} }$

$\tt{:\implies Simple \: Interest = \frac{460 \cancel{0} \times 1 \times \cancel{10}}{ \cancel{100}} }$

$\tt{:\implies Simple \: Interest =₹460 }$

Amount after 1 year:

$\tt{Amount =Simple \:Interest +Principle }$

$\tt{:\implies Amount =₹4600+₹460}$

$\tt{:\implies Amount =₹5,060}$

Year 2:

Here:

• P=₹5060(Amount of 1 year)
• R=12%
• T=1 year

Interest for 2 year:

$\tt{Simple \: Interest = \dfrac{P \times R \times T}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{5060 \times 12 \times 1}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{506 \cancel{0} \times 12 \times 1}{10 \cancel{0}} }$

$\tt{ :\implies Simple\:Interest = \dfrac{6,072}{10} }$

$\tt{ :\implies Simple\:Interest =₹ 607.2}$

Amount after 2 year:

$\tt{Amount = Simple \: Interest + P}$

$\tt{:\implies Amount = 607.2 + 5060}$

$:\implies \blue{\boxed{\tt{ Amount =₹ 5667.2}}}$

Compound Interest:

$\tt{Compound \: Interest =Final \: Amount- Initial \: \: P }$

$\tt{:\implies Compound \: Interest = 5667.2 - 4600 }$

$:\implies \blue{ \boxed{ \tt{Compound \: Interest =₹ \: 1067.2 }}}$

$\Large{\orange{ \bold{Part \: 2: }}}$

Year 1:

Here:

• P=₹16000
• R=10%
• T=1

Interest for 1 year:

$\tt{Simple \: Interest = \dfrac{P \times R \times T}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{16000 \times 10 \times 1}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{1600 \cancel0 \times \cancel{10} \times 1}{1 \cancel0 \cancel{0}} }$

$\tt{:\implies Simple \: Interest = ₹1600 }$

Amount after 1 year:

$\tt{:\implies Amount = 1600+16000 }$

$\tt{:\implies Amount = ₹17,600}$

Year 2:

Here:

• P= ₹17600(Amount of 1 year)
• R=14%
• T=1

Interest for 2 year:

$\tt{Simple \: Interest = \dfrac{P \times R \times T}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{17600 \times 14 \times 1}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{176 \cancel{00 }\times 14 \times 1}{ \cancel{100}} }$

$\tt{:\implies Simple \: Interest = 176 \times 14 }$

$\tt{:\implies Simple \: Interest = ₹ 2,464 }$

Amount after second year:

$\tt{Amount = Simple \: Interest + P}$

$\tt{:\implies Amount = 2464 + 17600}$

$\tt{:\implies Amount = ₹20,064}$

Year 3:

Here:

• P = ₹20,064
• R =15%
• T= 1

Interest for 3 year:

$\tt{Simple \: Interest = \dfrac{P \times R \times T}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{20064 \times 15 \times 1}{100} }$

$\tt{:\implies Simple \: Interest = \dfrac{300,960}{100} }$

$\tt{:\implies Simple \: Interest = 3009.60 }$

Amount after 3 year:

$\tt{Amount = Simple \: Interest + P}$

$\tt{Amount = 3009.60 + 20064}$

$:\implies \blue{\boxed{\tt{ Amount = ₹23,073.6}}}$

Compound Interest:

$\tt{Compound \: Interest =Final \: Amount- Initial \: \: P }$

$\tt{:\implies Compound \: Interest = ₹23,073.6 - 16000 }$

$:\implies \blue{ \boxed{ \tt{Compound \: Interest =₹7,073.6 \: }}}$