Question

Find the compound interest on 75000 for 2 years compounded annually at the rate of interest being 8% p.a.for the first year and 8.5% p.a for the second year. thanks​

Answer 1

Answer:

Amount = P + I = 81000 + 6885 = $87,885. C.I. = A - P = 87885 - 75000 = $12,885. ∴ Compound Interest is $12,885

Step-by-step explanation:

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Answer 2

Given :

• Principal = Rs.75000
• Rate for the 1st year = 8 %
• Rate for the 2nd year = 8.5 %

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To Find :

• Compound Interest = ?

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Solution :

~ Formula Used :

• Amount :

$\begin{gathered}\large{\color{darkblue}{\dashrightarrow}} \: \: {\underline{\boxed{\red{\sf{ A = P \bigg[1 + \dfrac{R}{100} \bigg]^n }}}}} \\ \end{gathered}$

• Compound Interest :

$\large{\color{darkblue}{\dashrightarrow}} \: \: {\underline{\boxed{\red{\sf{ C.I = Amount - Principal }}}}}$

Where :

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

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}}\end{gathered}$

~ Calculating the Amount :

$\begin{gathered} {\longmapsto{\qquad{\sf{ A = P \bigg[1 + \dfrac{R}{100} \bigg]^n \times \bigg[1 + \dfrac{R}{100} \bigg]^n }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \bigg[1 + \dfrac{8}{100} \bigg]^1 \times \bigg[1 + \dfrac{8.5}{100} \bigg]^1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \bigg[1 + \dfrac{8}{100} \bigg]^1 \times \bigg[1 + \dfrac{85}{1000} \bigg]^1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \bigg[1 + \cancel\dfrac{8}{100} \bigg]^1 \times \bigg[1 + \cancel\dfrac{85}{1000} \bigg]^1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \bigg[1 + 0.08 \bigg]^1 \times \bigg[1 + 0.085 \bigg]^1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \bigg[ 1.08 \bigg]^1 \times \bigg[ 1.085 \bigg]^1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \times 1.08 \times 1.085 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ A = 75000 \times 1.1718 }}}} \\ \\ \ {\qquad{\textsf{ Amount of this principal = {\purple{\sf{ ₹ \: 87885 }}}}}}\end{gathered}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}}\end{gathered}$

~ Calculating the Compound Interest :

$\begin{gathered}{\dashrightarrow{\qquad{\sf{ Compound \: Interest = Amount - Principal }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Compound \: Interest = 87885 - 75000 }}}} \\ \\ \ {\qquad{\textsf{ Compound Interest of this principal = {\green{\sf{ ₹ \: 12885 }}}}}}\end{gathered}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}}\end{gathered}$

Therefore :

❝ Compound interest on this principal is ₹ 12885 . ❞

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