Question

First Bank of Belmont offers a savings account with an APR of 5% with daily compounding. United Charlotte Bank offers a savings account with an APR of 5.1% with monthly compounding. Which bank would you prefer to use for your savings? Explain why (Use numbers! Be sure to explain why you prefer one number to the other number).

Answer 1

First Bank:

Effective annual rate = (1 + APR/n)^n - 1

Effective annual rate = (1 + 0.05/365)^365 - 1

Effective annual rate = (1 + 0.00014)^365 - 1

Effective annual rate = 1.0513 - 1

Effective annual rate = 0.0513 or 5.13%

United Bank:

Effective annual rate = (1 + APR/n)^n - 1

Effective annual rate = (1 + 0.051/12)^12 - 1

Effective annual rate = (1 + 0.00425)^12 - 1

Effective annual rate = 1.0522 - 1

Effective annual rate = 0.0522 or 5.22%

United Charlotte Bank should be preferred as it has the higher effective annual return. This means that you will get more in the form of interest if you save your money in United Charlotte Bank.