Question

You plan to invest some money in a bank account. Please compute the effective annual rates (EAR) for each bank below. Which of the following banks provides you with the highest effective rate of interest?

• Bank 1; 5.1% with annual compounding
• Bank 2; 5.0% with monthly compounding
• Bank 3; 5.0% with annual compounding
• Bank 4; 5.0% with quarterly compounding.
• Bank 5; 5.0% with daily (365-day) compounding

Answer 1

effective annual rate = (1+i/n)ⁿ - 1

i = interest rate and n = compounding frequency

Bank 1 - annual compounding means compounding frequency is once in a year. so effective annual rate is 5.1%.

Bank 2 - monthly compounding means compounding frequency is 12 times in a year.

effective annual rate = (1+0.05/12)¹² - 1 = (1+0.0041666666666667)¹² - 1 = 1.004166666666667¹² - 1 = 1.0512 - 1 = 0.0512 or 5.12%

Bank 3 - annual compounding means compounding frequency is once in a year. so effective annual rate is 5%.

Bank 4 - Quarterly compounding means compounding frequency is 4 times in a year as there are 4 quarters in a year.

effective annual rate = (1+0.05/4)⁴ - 1 = (1+0.0125)⁴ - 1 = 1.0125⁴ - 1 = 1.0509 - 1 = 0.0509 or 5.09%

Bank 5 - Daily compounding means compounding frequency is 365 times in a year. as there are 4 quarters in a year.

effective annual rate = (1+0.05/365)³⁶⁵ - 1 = (1+1.369863013698630136986301369863e-4)³⁶⁵ - 1 = 1.000136986301369863013698630137³⁶⁵ - 1 = 1.0513 - 1 = 0.0513 or 5.13%

Bank 5 provides you with the highest effective rate of interest of 5.13%.