5.6: Quoted versus Effective Rates Flashcards
What is the definition of the effective rate?
The effective rate is the rate at which a dollar invested grows over a given period, usually stated in percentage terms based on an annual period.
How is the future value (FV) calculated for an investment of $1,000 at a quoted annual rate of 16% compounded annually?
FV = $1,000 * (1.16)^1 = $1,160
How is the future value (FV) calculated for an investment of $1,000 at a quoted annual rate of 16% compounded quarterly?
FV = $1,000 * (1.04)^4 = $1,170 (rounded)
What is the formula to determine the effective annual rate (k) for any quoted annual rate (QR), given the compounding interval (m)?
k = (1 + QR / m)^m - 1
Calculate the effective annual rate (k) for a quoted rate (QR) of 16% compounded annually (m = 1).
k = (1 + 0.16 / 1)^1 - 1 = 16%
Calculate the effective annual rate (k) for a quoted rate (QR) of 16% compounded quarterly (m = 4).
k = (1 + 0.16 / 4)^4 - 1 = 17%
What is the effective annual rate for 12% compounded annually?
k = (1 + 0.12 / 1)^1 - 1 = 12%
What is the effective annual rate for 12% compounded semi-annually?
k = (1 + 0.12 / 2)^2 - 1 = 12.36%
What is the effective annual rate for 12% compounded quarterly?
k = (1 + 0.12 / 4)^4 - 1 = 12.55%
What is the effective annual rate for 12% compounded monthly?
k = (1 + 0.12 / 12)^12 - 1 = 12.68%
What is the effective annual rate for 12% compounded daily?
k = (1 + 0.12 / 365)^365 - 1 = 12.747%
What is the effective annual rate for 12% compounded continuously?
k = e^0.12 - 1 = 12.75%
What are the keystrokes to solve for the effective annual rate using a financial calculator for daily compounding?
- Press 2ND, then ICONV.
- Press 2ND, then CLR WORK.
- Enter NOM = 12.
- Enter C/Y = 365.
- Press ENTER, then ↓, ↓.
- Press CPT to get 12.747%.
How do you calculate the effective monthly rate (k_monthly) given an annual effective rate (k_annual)?
k_monthly = (1 + k_annual)^(1/12) - 1
Calculate the effective monthly rate for an annual effective rate of 12.36%.
k_monthly = (1.1236)^(1/12) - 1 = 0.0097588 or 0.97588%
What is the equation to determine the effective rate for any period, given any quoted rate?
k = (1 + QR / m)^f - 1
Why can effective rates often be very different from quoted rates?
Effective rates take into account the frequency of compounding, whereas quoted rates do not.
Explain how to calculate the effective rate for any period.
- Identify the quoted rate (QR) and the compounding frequency (m).
- Determine the frequency of payments per year (f) for the desired effective rate period.
- Use the formula: k = (1 + QR / m)^f - 1.
