Emma and Harry invested equal sums of money for 2 years. Emma invested in simple interest while Harry invested in compound interest. What should be the ratio of the rate of rate of interests if the interest received at the end is same?
Solution
Correct Answer: Option E
Let rate of interest in case of simple interest be M and that in compound interest be N.
We know, Simple interest = (Principal × Rate × Time)/100
And, Compound Interest = Principal \(\times \left[ {{{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)}^{\rm{T}}} - {\rm{\;}}1} \right]\)
If interest earned is same in 2 years,
⇒ (Principal × M × 2)/100 = Principal × (1 + N/100)2
⇒ M/50 = 1 + N2/10000 + N/50
With this equation, the ratio of M and N cannot be determined, as sum of degrees of M and N in each term is not same.
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