Discussion
A principal P becomes Q in 1 year when compounded annually with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded bi-monthly with S% annual rate of interest, then which one of the following is correct?
Answer: C
The correct relation is R > S.
Compounding more often makes money grow faster at the same nominal rate. Bi-monthly compounding (six times a year) at S% must produce the same amount Q in one year as annual compounding at R%, so S has to be the smaller rate.
\[ \begin{aligned} \left(1 + \frac{S}{600}\right)^{6} &= 1 + \frac{R}{100} \\ \Rightarrow S &\lt R \end{aligned} \]
For example, 10% compounded bi-monthly gives about 10.43% in a year. R = S would hold only if there were no compounding within the year, so \(R \le S\) and \(R \lt S\) are wrong, and the data are sufficient because the relation holds for every positive rate.
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