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 0.050%, a weekly compounded rate of 0.355%, a monthly compounded rate of 1.15%, a quarterly compounded rater of 4.25%, a semiannually compounded rate of 7.5%, or an annually compounded rate of 18%? What is the effective annual rate (EAR) of a daily compounded rate of 0.050%?

Choose an annually compounded rate of 18%

The effective annual rate (EAR) of a daily compounded rate of 0.050% is 0.05001%.

Explanation:

We need to find the effective annual rate of interest for each nominal interest and compare this for the different alternatives.

The effective annual rate of interest is the annual rate that if compounded once a year would give us the same result as the same result as the interest per period compounded a number of times a year.

Conversion of Nominal to Effective Interest Rate.

1. A daily compounded rate of 0.050%

Use a financial calculator to enter the data

P/YR = 365

Nominal interest = 0.050%

Thus Effective Interest rate = ?  0.05001%

2. A weekly compounded rate of 0.355%

Use a financial calculator to enter the data

P/YR = 52

Nominal interest = 0.355%

Thus Effective Interest rate = ? 0.3556 %

3. A monthly compounded rate of 1.15%

Use a financial calculator to enter the data

P/YR = 12

Nominal interest = 1.15%

Thus Effective Interest rate = ? 1.1561%

4. A quarterly compounded rater of 4.25%

Use a financial calculator to enter the data

P/YR = 4

Nominal interest = 4.25%

Thus Effective Interest rate = ? 4,32%

5. A semiannually compounded rate of 7.5%

Use a financial calculator to enter the data

P/YR = 2

Nominal interest = 7.5%

Thus Effective Interest rate = ? 7.64%

6. an annually compounded rate of 18%

Use a financial calculator to enter the data

P/YR = 1

Nominal interest = 18%

Thus Effective Interest rate = ? 18%

Conclusion :

Choose the  option giving the HIGHEST effective annual rate.

Thu, I would rather have an annually compounded rate of 18%.