Which of the following is the better investment? \( 2.62 \% \) compounded monthly OR The investments will earn the same. The \( 2.62 \% \) compounded monthly is better. The \( 2.8 \% \) compounded annually is better. A comparison cannot be made unless the amount invested is known.

To evaluate which investment is better, we need to compare the effective annual rates (EAR) of both options. The \(2.62\%\) compounded monthly can be calculated using the formula \(EAR = (1 + r/n)^{nt} - 1\), where \(r\) is the nominal rate, \(n\) is the number of compounding periods, and \(t\) is the number of years (which will be 1 for comparison). This gives an EAR of about \(2.69\%\), which is greater than \(2.8\%\) compounded annually, making the latter the better choice! In practice, understanding compounding frequency is crucial when assessing investment options. Monthly compounding may seem beneficial, but if the annual percentage rate is higher and compounded less frequently, it could lead to better returns. Always convert to the effective annual rate to make direct comparisons!