Discussion
What will be ratio of simple to compound interest on two same sums invested in SBI at rate of interest of 8% kept for 3 years?
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Take the common sum as \( P \). Over 3 years at 8%:
\[ \text{SI} = P \times 0.08 \times 3 = 0.24P \]
\[ \text{CI} = P\left[(1.08)^{3} - 1\right] = P(1.259712 - 1) = 0.259712P \]
\[ \frac{\text{SI}}{\text{CI}} = \frac{0.24}{0.259712} = \frac{240000}{259712} = \frac{1875}{2029} \]
The sum cancels, so the ratio holds for any principal. Compound interest is always the larger of the two beyond the first year, so the ratio must be less than 1.
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