Question

Calculate the amount and the compound interest for the second year on ₹8000 invested for 3 years at 15% p.a. Also find the sum due at the end of third year.​

Answer 1

Given :

• Principal = Rs.8000
• Rate = 15 %
• Time = 3 years

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To Find :

• Amount for 2nd year = ?
• Compound interest for 2nd year = ?
• Amount at the end of 3rd year = ?

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Solution :

~ Formula Used :

• ${\underline{\boxed{\red{\sf{ A = P \bigg\lgroup 2 + \dfrac{R}{100} \bigg\rgroup ^n }}}}}$

• ${\underline{\boxed{\red{\sf{ C.I = Amount - Principal }}}}}$

Where :

• ➢ A = Amount
• ➢ P = Principal
• ➢ C.I = Compound Interest
• ➢ R = Rate
• ➢ n = Time

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~ Calculating the Amount for 2nd year :

${\longmapsto{\qquad{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup ^n }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + \dfrac{15}{100} \bigg\rgroup ^2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + \cancel\dfrac{15}{100} \bigg\rgroup ^2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + 0.15 \bigg\rgroup ^2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1.15 \bigg\rgroup ^2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \times 1.15 \times 1.15 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \times 1.3225 }}}} \\ \\ \ {\qquad{\green{\sf{ Amount \; for \; the \; Second \; year = ₹ \; 10580 }}}}$

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~ Calculating the Compound Interest for 2nd year :

${\dashrightarrow{\qquad{\sf{ Compound \; Interest = Amount - Principal }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Compound \; Interest = 10580 - 8000 }}}} \\ \\ \ {\qquad{\pink{\sf{ Compound \; Interest \; for \; the \; Second \; year = ₹ \; 2580 }}}}$

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~ Calculating the Amount at the End of 3rd year :

${\longmapsto{\qquad{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup ^n }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + \dfrac{15}{100} \bigg\rgroup ^3 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + \cancel\dfrac{15}{100} \bigg\rgroup ^3 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1 + 0.15 \bigg\rgroup ^3 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \bigg\lgroup 1.15 \bigg\rgroup ^3 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \times 1.15 \times 1.15 \times 1.15 \times 1.15 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 8000 \times 1.520875 }}}} \\ \\ \ {\qquad{\orange{\sf{ Amount \; for \; the \; Third \; year = ₹ \; 12167 }}}}$

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~ Therefore :

❛❛ Compound interest at the end of 2nd year is ₹ 2580 and the amount is ₹ 10580 .Amount at the end of 3rd year is ₹ 12167 . ❜❜

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Answer 2

Compound interest for the second year will be the simple interest gained in the second year, with the amount after first year being the principal for the second year.

For the first year

P=Rs8,000

N=1year

R=10 %

We have S.I.=

100

PNR

=

100

8,000×1×10

=Rs800

And Amount at the end of first year P+S.I.=Rs8,000+Rs800=Rs8,800

Now, for the second year

P=Rs8,800

N=1year

R=10 %

We have S.I.=

100

PNR

=

100

8,800×1×10

=Rs880

Thus, Compound interest for the second year =Rs880