Calculating Maximum Effective Annual Rate with Continuous Compounding

How can a bank maximize its earnings from an APR of 7.65% through continuous compounding?

The bank can maximize its earnings by calculating the Maximum Effective Annual Rate (EAR) using continuous compounding.

When a bank offers an Annual Percentage Rate (APR) of 7.65% on its loans, it has the opportunity to earn more through continuous compounding. Continuous compounding allows the bank to earn compound interest on interest continuously throughout the year, resulting in a higher effective rate of return.

To calculate the Maximum Effective Annual Rate (EAR) with continuous compounding, we use the formula EAR = e^(r) - 1, where 'e' is the mathematical constant approximately equal to 2.71828 and 'r' is the APR expressed as a decimal.

For the given APR of 7.65%, we convert it to a decimal by dividing by 100, which gives us 0.0765. Plugging this value into the formula, we get EAR = e^(0.0765) - 1, which results in an approximate EAR of 7.95%.

Therefore, by utilizing continuous compounding and calculating the Maximum Effective Annual Rate, the bank can maximize its earnings beyond the quoted APR of 7.65%.