Interest Rates Flashcards
What is the Effective Annual Rate (EAR)?
The actual amount of interest that will be earned at the end of one year
What is the equation for an equivalent n-period discount rate?
-[(1+r)^n]-1
-n can be larger or smaller than 1 depending on the period over which the interest is being calculated for
What is the Annual Percentage Rate (APR)
-This indicates the amount of simple interest earned in the period without any compounding
-APR with monthly compounding is actually a way of quoting the monthly interest rate rather than the annual rate
-As this will often be higher than the actual APR, you cannot use the APR itself as a discount rate
What is the equation for APR with monthly compounding?
Interest Per Compounding Period= [(APR)/ (k periods/year)]
How do you convert between APR and EAR?
-1 +EAR= [1+(APR/k)^k]
-EAR= [1+(APR/k)^k]-1
-Continuously decreasing the compounding period is continuous compounding
-Compounding more frequently than aily has a negligible impact on the EAR
What two steps should be taken when working with APRs?
- Divide the APR by the number of compounding period per year to determine the actual interest rate per compounding period
- Compute the appropriate discount rate by compounding
What is the process and what considerations need to be taken when computing loan payments?
- Equate the outstanding loan balance with the present value of the loan using the quoted discount rate
- Solve for the loan payment
- Amortising loans are when each month you pay interest on the loan plus some part of the loan balance
- If the APR is not explicitly stated then it is equal to the interval between payments
What is the equation for computing loan payments
C= P/ [(1/r)*(1-1/r^n)]
C= Monthly loan payment
P= Principal Value
r= APR adjusted interest rate for compounding
n= Number of months
What is the nominal interest rate?
The nominal interest rate is the rate at which money will grow if invested for a certain period
What is the real interest rate?
The growth of purchasing power adjusted for inflation
What is the equation for the real interest rate?
r= (r-i)/ (1+i)= r-i
What is the term structure of interest rates?
-The relationship between the investment term and the interest rate
-The interest rate charged on loans depends on the term of the investment
What is the yield curve?
The yield curve is the combination of points for different terms and EAR’s for given terms
How do you calculate the present value of a payment using term structure discounts?
PV= C/ (1+r)^n
-r= risk free interest rate
How do you calculate the present value of a cash flow stream using term structure discount rates?
-Discount each cash flow separately using the appropriate discount rate and n
-Sum all cash flows
What happens to the relationship between long-term and short-term interest rates if interest rates are expected to rise?
Long-term interest rates will be shorter than short-term interest rates
What happens to the relationship between long-term and short-term interest rates if interest rates are expected to fall?
-Long-term interest rates will be lower than short-term interest rates
-This is to attract borrowers
What does a steep yield curve imply?
This implies that interest rates are expected to rise in the future
What does an inverted yield curve imply?
This implies that interest rates are expected to fall
What is the relationship between risk and interest rates?
-Different borrowers have different associated risks of default
-Interest rates depend on the identity of the borrower
-Reliable borrowers (e.g. US government) have very low interest rates
-All other borrowers have higher interest rates as they have some risk of default
-The interest rate stated on these loans is the maximum amount investors will receive if no default
-To compensate for the risk of default, investors may demand higher returns and therefore higher interest rates
What is the equation for after-tax interest?
r-tr=r (1-t)
What is the opportunity cost of capital?
This is the best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted
