In the first Early Bird webinar, we reviewed compound frequencies. I created below a simple sheet to give practice in conversions; e.g., from discrete to continuous.

Here are fourteen practice questions. The answers are in the EditGrid spreadsheet below, but of course, it’s good to work them out yourself. The answers are highlighted in green cells.

• If rate is quoted as 10% per annum with semiannual compounding, what is equivalent rate under continuous compounding (Hull example 4.1)?
• If rate is quoted as 8% per annum with continuous compounding, but interest is paid quarterly. What is equivalent rate with quarterly compounding? (Hull example 4.2)?
• If rate is 8% per annum with continuous compounding, what is the discount factor for a cash flow received in three (3) years?
• If rate is 9% per annum with continuous compounding, what is the future value of today’s $1 dollar at the end of five (5) years?
• If rate is quoted as 10% per annum with daily compounding (assume 252 trading days/year), what is equivalent rate under continuous compounding?
• If rate is quoted as 11% per annum with continuous compounding, but interest is paid monthly (m=12). What is equivalent rate with monthly compounding?
• If a future cash flow in an interest rate swap will be received in three (3) years, what is the discount factor if we assume continuous compounding and an interest rate of 7%?
• If the rate is 8% per annum with annual compounding, what is the discount factor for a cash flow received in ten (10) years?
• Convert a 12% continuous interest rate into its semi-annual (discrete) equivalent.
• Convert a 12% monthly (discrete) interest rate into continuous equivalent.
• What is the price of a ten-year (10 year maturity) zero-coupon bond with $100 face value, if the interest rate is 6% under continuous compounding?
• What is the price of a twenty-year (20 year maturity) zero-coupon bond with $100 face value, if the interest rate is 9% under continuous compounding?
• What is the price of a ten-year (10 year maturity) zero-coupon bond with $100 face value, if the interest rate is 6% under semi-annual compounding?
• What is the price of a twenty-year (20 year maturity) zero-coupon bond with $100 face value, if the interest rate is 9% under semi-annual compounding?
• Bonus fun #1. Convert a bond-equivalent yield of 6% (i.e., semi-annual compounding) into its quarterly equivalent?
• Bonus fun #2. Convert a bond-equivalent yield of 9% (i.e., semi-annual compounding) into its monthly equivalent?

Spreadsheet:

Comments

1. fashepard 14 Feb 2009

   Thanks for these problems.  this was very helpful to me. It is always better to see it in a question. will review this several times.  Thanks David

   Frank

2. David Harper, CFA, FRM, CIPM 14 Feb 2009

   Frank, that’s great, glad you find helpful. I need to do problems, too, to make it concrete. David

3. fashepard 17 Feb 2009

   David,

   On bonus fun #1 and #2 .  I am having writing the formula
   from the spread sheet.  I guess there are to many ((())) for me
   Can you write it out?

4. fashepard 17 Feb 2009

   OK David.  I got it

   Frank

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