Calculate the effective annual rate with continuous compounding

What is the effective annual rate if a bank offers 7.50% on savings accounts compounded continuously?

Options: a) 7.59% b) 7.60% c) 7.61% d) 7.62%

Answer:

The effective annual rate when interest is compounded continuously is approximately 7.61%.

Calculating the effective annual rate when interest is compounded continuously involves using the formula:

EAR = e^(r) - 1

Where r is the annual interest rate in decimal form. In this case, the annual interest rate is 7.50%, which is equivalent to 0.075 in decimal form. Plugging in the values, we get:

EAR = e^(0.075) - 1

Using a calculator to find the value of e^(0.075) and subtracting 1, we get the effective annual rate to be approximately 7.61% (option c).