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AFCAT Model Paper 6

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Question : 55 of 100

Marks: +1, -0

Find the sum of money on which the difference between the compound interest (compounded annually) and the simple interest at the same rate of 5% per annum after 2 years is Rs. 10?

Rs. 1000
Rs. 2000
Rs. 3000
Rs. 4000

Solution:

Given:

Difference between the compound and the simple interest is Rs. 10

Rate = 5% and Time = 2 years

Formula Used:

Compound Interest

=P\left[\left(1+\frac{\text{Rate}}{100}\right)^{\text{Time}}-1\right]

Where, P = Principal

Simple Interest

=\frac{PRT}{100}

Calculation:

Let the sum of money be Rs. ‘P’

According to the question

CI – SI = 10

\Rightarrow P\left[\left(1+\frac{\text{Rate}}{100}\right)^{\text{Time}}-1\right]-\left[\frac{P \times \text{Rate} \times \text{Time}}{100}\right]=10

⇒

P\left[\left(1+\frac{5}{100}\right)^{2})-1\right]-\left[\frac{P \times 5 \times 2}{100}\right]=10

⇒

P[(1.05)^{2}-1]-0.1P=10

⇒ 0.1025P – 0.1P = 10

⇒ 0.0025P = 10

⇒ P

=\frac{10}{0.0025}=4000

∴ Required sum = Rs. 4000

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