The compound interest on a sum of Rs. 20,000 at 15% p.a. for \(2 \fra

1.	The compound interest on a sum of Rs. 20,000 at 15% p.a. for \(2 \frac{2}{3}\)years, when interest compounded yearly is:1. Rs. 9,0002. Rs. 9,0953. Rs. 9,9084. Rs. 8,896
Answer» Correct Answer - Option 2 : Rs. 9,095 Given: Principal = Rs. 20000, Rate = 15%, Time = \(2\frac{2}{{3\;}}\;{\rm{years}}\) Formula used: Amount = Principal(1 + rate/100)^time Calculation: Amount = Principal(1 + rate/100)^time \(\Rightarrow 20000 \times {\left( {1 + \;\frac{{15}}{{100}}} \right)^2}\left( {1 + \;\frac{{\frac{2}{3} \times 15}}{{100}}} \right)\) \(\Rightarrow 20000 \times {\left( {\;\frac{{23}}{{20}}} \right)^2}\left( {\;\frac{{11}}{{10}}} \right)\) ⇒ 5 × 23 × 23 × 11 ⇒ 29095 Interest = Amount – Principal ⇒ 29095 – 20000 ⇒ 9095 ∴ The compound interest is Rs. 9095.

The compound interest on a sum of Rs. 20,000 at 15% p.a. for \(2 \frac{2}{3}\)years, when interest compounded yearly is:1. Rs. 9,0002. Rs. 9,0953. Rs. 9,9084. Rs. 8,896

Answer» Correct Answer - Option 2 : Rs. 9,095

Given:

Principal = Rs. 20000, Rate = 15%, Time = \(2\frac{2}{{3\;}}\;{\rm{years}}\)

Formula used:

Amount = Principal(1 + rate/100)^time

Calculation:

Amount = Principal(1 + rate/100)^time

\(\Rightarrow 20000 \times {\left( {1 + \;\frac{{15}}{{100}}} \right)^2}\left( {1 + \;\frac{{\frac{2}{3} \times 15}}{{100}}} \right)\)

\(\Rightarrow 20000 \times {\left( {\;\frac{{23}}{{20}}} \right)^2}\left( {\;\frac{{11}}{{10}}} \right)\)

⇒ 5 × 23 × 23 × 11

⇒ 29095

Interest = Amount – Principal

⇒ 29095 – 20000

⇒ 9095

∴ The compound interest is Rs. 9095.

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