Find the amount and compound interest on Rs.9000 for 2 years 4 months at 10% per annum compounded annually. The compound interest is ____.

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Detailed Solution

We are given the principal amount, rate of interest and the time and we have to find the amount and interest.
Given is,
1) P=9000
2) R=10%
3) N=2 years 4 months
Mathematically, time can be represented as -

N = 2 + \frac{4}{12} = 2 + \frac{1}{3} = \frac{7}{3} years

Now, we can put all the information in the formula.

A = P {(1 + \frac{R}{100})}^{n}

\Rightarrow A = 9000 {(1 + \frac{10}{100})}^{\frac{7}{3}}

Shortcut for calculation: If we write

\frac{7}{3}

in decimals, we will get 2.33333. It simply means 2 and

\frac{1}{3}

times. So, we will multiply

(1 + \frac{11}{10})

two times and for that

\frac{1}{3}

rd part, we will multiply

(1 + \frac{11}{10}) by \frac{1}{3}

in the shown way.
Moving back to the question,

\Rightarrow A = 9000 {(1 + \frac{10}{100})}^{2} (1 + \frac{\frac{1}{3} \times 10}{\frac{100}{1}})

Simplifying the equation,

\Rightarrow A = 9000 \times \frac{11}{10} \times \frac{11}{10} \times (1 + \frac{1}{30})

\Rightarrow A = 9000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{31}{30}

On multiplying and dividing, we will get –
⇒A= 11253
Therefore, the final amount is Rs.11,253.
In order to find the compound interest, we will have to subtract the principal amount from the final amount.
⇒C.I = A−P
⇒C.I = 11253−9000 = 2253
Hence, compound interest is Rs.2253.

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