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).