Emi invested profits of $10 000 into a savings account that earns interest compounding fortnightly, for one year.

The effective interest rate, rounded to two decimal places, is 5.07%.

Assume that there are exactly 26 fortnights in a year.

1. What is the nominal percentage rate of interest for the account?
2. Round your answer to two decimal places.   (1 mark)
   

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2. Explain why the nominal interest rate appears lower than the effective interest rate.  (1 mark)
   

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Consider the following four statements regarding nominal and effective interest rates as they apply to compound interest investments and loans:

• An effective interest rate is the same as a nominal interest rate if interest compounds annually.
• Effective interest rates increase as the number of compounding periods per year increases.
• A nominal rate of 12% per annum is equivalent to a nominal rate of 1% per month.
• An effective interest rate can be lower than a nominal interest rate.

How many of these four statements are true?

1. 0
2. 1
3. 2
4. 3
5. 4

The nominal interest rate for a loan is 8% per annum.

When rounded to two decimal places, the effective interest rate for this loan is not

1. 8.33% per annum when interest is charged daily.
2. 8.32% per annum when interest is charged weekly.
3. 8.31% per annum when interest is charged fortnightly.
4. 8.30% per annum when interest is charged monthly.
5. 8.24% per annum when interest is charged quarterly.

Millie invested $20 000 in an account at her bank with interest compounding monthly.

After one year, the balance of Millie’s account was $20 732.

The difference between the rate of interest per annum used by her bank and the effective annual rate of interest for Millie’s investment is closest to

1. 0.04%
2. 0.06%
3. 0.08%
4. 0.10%
5. 0.12%