Question

Periodic interest rates.

You have a savings account in which you leave the funds for one year without adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of 0.055%, a weekly compounded rate of 0.305%, a monthly compounded rate of 1.55%, a quarterly compounded rate of 4.50%, a semiannually compounded rate of 7%, or an annually compounded rate of 17%?

Calculate the EAR for each of the possible rates.

Answer 1

1)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.00055)³⁶⁵ - 1

EAR = 1.2223 - 1

EAR = 0.2223 or 22.23%

2)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.00305)⁵² - 1

EAR = 1.1716 - 1

EAR = 0.1716 or 17.16%

3)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.0155)¹² - 1

EAR = 1.2027 - 1

EAR = 0.2027 or 20.27%

4)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.045)⁴ - 1

EAR = 1.1925 - 1

EAR = 0.1925 or 19.25%

5)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.07)² - 1

EAR = 1.1449 - 1

EAR = 0.1449 or 14.49%

6)

EAR = (1 + rate)ⁿ - 1

EAR = (1 + 0.17)¹ - 1

EAR = 1.17 - 1

EAR = 0.17 or 17%

The best possible rate is the monthly compounded rate of 0.055% as it has the highest EAR