Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years at a certain rate per annum, when the interest is compounded yearly. The rate of interest is:
Option 1: 12%
Option 2: 15%
Option 3: 20%
Option 4: 8%

Question

Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years, at a certain rate per cent per annum when the interest is compounded yearly. If INR 10,000 at the same rate of interest is borrowed for two years, then what will be the compound interest (in INR)?

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Answer 1

Correct Answer: 12%

Solution : Let $P$ be the principal sum and $R$ be the interest rate.
Total amount after $n$ years, compounded annually = $P (1 + \frac{R}{100})^{n}$
Total amount after 4 years = INR 7,562
$P (1 + \frac{R}{100})^{4} = 7562$ -------------(i)
Total amount after 5 years = INR 8,469.44
$P (1 + \frac{R}{100})^{5} = 8469.44$ -------------(ii)
Dividing (ii) by (i),
$1 + \frac{R}{100} = \frac{8469.44}{7562}$
⇒ $1 + \frac{R}{100} = 1.12$
⇒ $\frac{R}{100} = 0.12$
⇒ $R = 0.12 \times 100 = 12$ %
Hence, the correct answer is 12%.

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Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years at a certain rate per annum, when the interest is compounded yearly. The rate of interest is:Option 1: 12%Option 2: 15%Option 3: 20%Option 4: 8%

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Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years at a certain rate per annum, when the interest is compounded yearly. The rate of interest is:
Option 1: 12%
Option 2: 15%
Option 3: 20%
Option 4: 8%