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

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Answer 1

Given :

• Principal = ₹ 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 :

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

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

Where :

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

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~ Calculating the Amount :

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

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~ Calculating the Compound Interest :

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

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Therefore :

❝ Compound interest on this principal is ₹ 12885 . ❞

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Answer 2

Answer:

$12,885.

Step-by-step explanation:

This problem is solved by S.I. Method.

Given that,

Principal = $75,000.

Time = 2years.

Rate₁ = 8% p.a.

Rate₂ = 8.5% p.a.

Compounded - Annually

For the 1st year

Principal = $75,000.

Time = 1year.

Rate = 8% p.a.

$\:\:\:\:\:\:\boxed{\rm{I =\frac{P \times R \times T}{100}}} \\ \\ \\:\implies\rm{I = \frac{75000 \times 8 \times 1}{100}} \\ \\ \\:\implies\rm{I = \frac{750\cancel{00}\times 8 \times 1}{1 \cancel{00}}} \\ \\ \\:\implies\rm{I = 750 \times 8} \\ \\ \\\therefore\rm\:Simple \: Interest =\ 6,000.$

Amount = P + I = 75000 + 6000 = $81,000.

For the 2nd year

Amount(1st year) = Principal(2nd year)

Principal = $81,000.

Time = 1year.

Rate = 8.5% p.a.

$\:\:\:\:\:\:\boxed{\rm{I = \frac{P \times R \times T}{100}}} \\ \\ \\:\implies\rm{I = \frac{81000 \times 8.5 \times 1}{100}} \\ \\ \\:\implies\rm{I = \frac{810\cancel{00} \times 8.5 \times 1}{1\cancel{00}}} \\ \\ \\:\implies\rm{I =810 \times 8.5} \\ \\ \\:\implies\rm{810 \times \frac{85}{10}} \\ \\ \\:\implies\rm{81\cancel0 \times \frac{85}{1\cancel0} } \\ \\ \\:\implies\rm{81 \times 85} \\ \\ \\\therefore\rm{Simple \: Interest = \ 6,885.}$

Final Amount = P + I = 81000 + 6885

= $87,885.

C.I. = Final Amount - Original Principal = 87885 - 75000 = $12,885.

∴ Compound Interest is $12,885.

Used Abbreviations

P = Principal.

A = Amount.

C.I. = Compound Interest.

S.I. = Simple Interest.

I = Simple Interest.

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