Chapter 5: Interest Rates
periodic interest rate
the annual percentage rate divided by the number of compounding periods per year r = apr / m
As you increase the compounding frequency, the future value will:
increase
compounding period
the period in which interest is applied
Interest premium. Shaky Company has just issued a five-year bond with a yield of 9%; Stable Company has issued an identical five-year bond, but with a yield of 7%. Why did the market demand a higher return from Shaky?
Companies with poor financials tend to compensate investors for the default risk by issuing bonds with high yields.
If we want to get some idea about a default premium over time between two specific assets, we can compare the returns on short−term or medium−term bonds with those on large company stocks.
False
Firms A and B both issued 20-year bonds on the same date that have identical features except for the coupon rates. However, Firm A bonds have a coupon rate of 5% and Firm B bonds have a coupon rate of 7%. This difference is due to:
Firms A and B both issued 20-year bonds on the same date that have identical features except for the coupon rates. However, Firm A bonds have a coupon rate of 5% and Firm B bonds have a coupon rate of 7%. This difference is due to Firm B having a higher probability of default. Since both bonds are identical in all other respects the interest rate differential can only be due to differences in default risk. Firm B obviously has a higher risk of default which forces the firm to pay a higher coupon rate of interest to compensate bond buyers for that risk. Both bonds are impacted by inflation rates in the same manner.
The Fisher Effect involves which of the items below?
Nominal rate, the real rate, and inflation
Which of the following statements is TRUE?
On many calculators the TVM key for interest is I/Y; this is Interest per Year, or the APR rate.
The historically low Treasury bill rates between 2008 and 2013 reflect the Federal Reserve's action to stimulate the economy following the 2008 financial meltdown.
True
The "Truth in Savings Law" requires banks to advertise their rates on investments such as CDs and savings accounts as annual percentage yields (APY).
True
Some financial advisors recommend making one extra mortgage payment per year since the extra payment:
all goes toward principal reduction.
The ________ compensates the investor for the additional risk that the loan will not be repaid in full.
default premium
APRs must be converted to the appropriate periodic rates when compounding is ________.
more frequent than once a year
Titan State Bank offers to pay you 6% interest, compounded quarterly. The 6% interest rate is known as the:
nominal interest rate
The stated rate of interest on a loan is the __________.
nominal interest rate The nominal rate of interest = real rate of interest + rate of inflation.
The yield curve refers to a curve constructed with:
time to maturity on the x-axis and interest rate on the y-axis. The yield curve refers to a curve constructed with time to maturity on the x-axis and interest rate on the y-axis. In order to isolate the maturity premium the yield curve needs to be comprised of bonds from the same issuer such as the U.S. government. Bonds from the same issuer should have approximately the same level of default risk.
We can write the true relationship between the nominal interest rate and the real rate and expected inflation as:
.r = (1 + r*) × (1 + h) − 1
Aakash just bought a house for $145,000 and financed 100% of the amount using a 6% fixed-rate 30-year mortgage. Assuming monthly payments, how long will it take him to pay off the loan if he decides to pay $100 a month over his required minimum payment?
Aakash just bought a house for $145,000 and financed 100% of the amount using a 6% fixed-rate 30-year mortgage. Assuming monthly payments, it will only take him 23 years to pay off the loan if he decides to pay $100 a month over his required minimum payment. To find the correct answer you need to compute Aakash's required minimum payment using your financial calculator. The correct inputs are; PV = -$145,000; FV = 0; N = 360; I/Y = 6/12 = .5; CPT PMT = $869.35. Now you can solve for the time it will take him to pay off the loan if he adds $100.00 to his monthly payment using the following inputs; PMT = $869.35 + $100.00 = $969.35; PV = -$145,000; FV =0; I/Y = .5; CPT N = 276.29 months. When you divide the months by 12 you get 23 years (i.e. 276.29/12 = 23.02 years).
A(n) __________ yield curve is downward sloping and to the right which means that short-term interest rates are __________ than long-term interest rates.
An inverted yield curve is downward sloping and to the right which means that short-term interest rates are higher than long-term interest rates. An inverted yield curve is typically interpreted to mean a slowing economy so investors are willing to take a lower rate on longer term financial instruments. A normal yield curve is upward sloping and to the right which means long-term interest rates are higher than short-term interest rates. A segmented yield curve shows interest rates alternating between higher and lower rates as time to maturity increases.
As you increase the compounding frequency, holding all else constant, the effective annual rate:
As you increase the compounding frequency, holding all else constant, the effective annual rate increases. This is because more frequent compounding means the interest earned is added back to the principal more often and any subsequent interest is earned on the new higher amount. The more frequently that process occurs the more money you will have at the end of the year. Therefore, a higher compounding frequency will increase your effective annual rate of return. This will always be the case for any non-zero interest rate.
A company selling a bond is ________ money.
Borrowing
Brenda borrows $3,000 from Mountain State Bank. The interest rate on the loan is 6.1%, compounded quarterly. The effective annual rate (EAR) on the loan is:
Brenda borrows $3,000 from Mountain State Bank. The interest rate on the loan is 6.1%, compounded quarterly. The effective annual rate (EAR) on the loan is 6.2%. You need to use the following formula to calculate EAR: Where the APR is the stated loan rate and m is the compounding frequency. So, the EAR for Brenda's loan is: The EAR will always be greater than the stated or quoted rate on a loan if it compounds more frequently than annually. For annual compounding, the EAR will be equivalent to the stated rate.
Cambridge State Bank is paying 7% interest on its one-year certificates of deposit. If the inflation rate is 4%, which of the following is the best approximation for the real rate of interest that Cambridge State Bank is paying?
Cambridge State Bank is paying 7% interest on its one-year certificates of deposit. If the inflation rate is 4%, the best approximation for the real rate of interest that Cambridge State Bank is paying is 3%. The nominal or stated rate of interest can be viewed as the real rate plus an inflation premium so, Nominal rate = real rate of interest + expected inflation premium Given the nominal rate of 7% and an inflation rate of 4%, we can simply plug those numbers into the simple formula and solve for an approximation of the real interest rate. So, 7% = real rate + 4% Real rate = 3%
Over the past 65 years, the highest rate of interest on three-month Treasury bills occured in:
Over the past 65 years, the highest rate of interest on three-month Treasury bills occurred in 1981, approaching 15%. However, the Federal Reserve adopted a contractionary monetary stance that reduced interest rates and inflation over the next several years.
The relationship between nominal interest rates, real interest rates and inflation is known as the:
Fisher effect. The relationship between nominal interest rates, real interest rates and inflation is known as the Fisher effect. The Fisher effect is named after economist Irving Fisher who is credited with being the first to quantify the relationship that shows that nominal interest rates = real rate + inflation rate + (real rate x inflation).
If the inflation rate is 6 percent and the nominal rate of interest is 4 percent, then the real interest rate is __________.
If the inflation rate is 6 percent and the nominal rate of interest is 4 percent, then the real interest rate is -2 percent. The real rate is equal to the nominal rate minus the rate of inflation so the real rate = 4% - 6% = -2%. This is how inflation harms savers. A saver will lose 2 percent of their purchasing power by keeping money in the bank drawing the nominal return.
Which of these statements about interest rates and inflation is true?
If there is zero inflation, the nominal interest rate is equal to the real interest rate. If there is zero inflation, the nominal interest rate is equal to the real interest rate. This is because the nominal interest rate (also called the stated or quoted interest rate) is equal to the real interest rate plus the rate of inflation. Savers will demand a real return which means some return over and above the rate of inflation, so that they can at least maintain the same level of purchasing power plus a small return.
In finance, __________ are often used as a proxy for the risk-free interest rate.
In finance, U.S. Treasury bills are often used as a proxy for the risk-free interest rate. U.S. Treasury bills have no default risk since they are backed by the U.S government and they are also very short-term so are not subject to any risk associated with time to maturity. And, any expected inflation should be embedded in the interest rates so that total returns are determined by the real rate and the inflation rate. Certificates of deposit are not used as a proxy for the risk-free rate although very short-term CDs should pay approximately the same interest rate. U.S. Treasury bonds are longer term and subject to maturity risk.
In general, if the loan's collateral is __________ in value, the default premium will be __________.
In general, if the loan's collateral is increasing in value, the default premium will be lower. Collateral is any asset that is pledged against the loan that can be seized and sold by the lender in the event the borrower defaults. If the collateral is increasing in value it lowers the default risk to the lender. Borrowers are much less likely to default on a loan when the value of the collateral exceeds the remaining loan balance.
Jason borrowed $5,000 from the First State Bank. The interest rate on his loan was 8% compounded quarterly. The effective annual rate on the loan is:
Jason borrowed $5,000 from the First State Bank. The interest rate on his loan was 8% compounded quarterly. The effective annual rate on the loan is 8.24%. The effective annual rate (EAR) formula is: Where, the APR is the stated loan rate and m is the compounding frequency. So, the EAR for Jason's loan is: The EAR will always be greater than the stated or quoted rate on a loan if it compounds more frequently than annually. For annual compounding, the EAR will be equivalent to the stated rate.
Jessica wants to save $100,000 in the next 10 years so she can have a good start on her retirement fund. How much will her monthly contributions need to be if she can earn a 12% return on her money?
Jessica wants to save $100,000 in the next 10 years so she can have a good start on her retirement fund. Her monthly contributions will need to be $434.71 if she can earn a 12% return on her money. You can solve this problem using your financial calculator and the following key strokes; $100,000 FV; 0 PV; 120 N; 12/12 = 1% I/Y; CPT PMT = -$434.71. Note that the answer is a negative number since we used a positive number for the future value.
Kramer Manufacturing would like to purchase a warehouse for $450,000. The monthly payment will be $4,556.03 if Kramer can finance the warehouse for 10 years at a 4% annual interest rate. How much of the first payment is interest?
Kramer Manufacturing would like to purchase a warehouse for $450,000. The monthly payment will be $4,556.03 if Kramer can finance the warehouse for 10 years at a 4% annual interest rate. The interest component of the first payment is $1,500.00. To compute the interest you simply multiply the principal balance by the periodic interest rate. In this example the periodic rate is a monthly rate equal to .04/12 months = .0033333. So, $450,000 x .00333333 = $1,500.00
The Truth in Lending Act of 1968 mandates banks quote loan rates as an __________ which effectively __________ the true cost of the loan if the compounding frequency is more than one time a year.
The Truth in Lending Act of 1968 mandates banks quote loan rates as an APR which effectively understates the true cost of the loan if the compounding frequency is more than one time a year. Increasing the compounding frequency of a loan pushes the actual cost (EAR or APY) higher due to the fact that the interest begins earning interest from the perspective of the lender or saver.
We assign a very low probability of default to the U.S. Treasury and thus assume that all Treasury bills will be paid in full at maturity and thus have a zero default premium.
True
When quoting rates on loans, the "Truth in Lending Law" requires the bank to state the rate as an APR, effectively understating the true cost of the loan when interest is computed more often than once a year.
True
Kramer Manufacturing would like to purchase a warehouse for $450,000. How much will the monthly payment be if Kramer can finance the warehouse for 10 years at a 4% annual interest rate?
Kramer Manufacturing would like to purchase a warehouse for $450,000. The monthly payment will be $4,556.03 if Kramer can finance the warehouse for 10 years at a 4% annual interest rate. You can solve for the payment by using the following keystrokes on your financial calculator; PV = -$450,000; FV = 0; N = 10 years x 12 months = 120; I/Y = 4/12 = .33333; CPT PMT = $4,556.03.
compounding periods per year (C/Y or M)
The frequency of times interest is added to an account each year
What is the true nominal interest rate if the real return is 5% and the expected rate of inflation is 7%?
The true nominal interest rate is 12.35% if the real return is 5% and the expected rate of inflation. Using the Fisher equation we can compute the true nominal rate by the following formula: r = r* + h +(r* x h) where: r = true nominal interest rate r* = real rate h = inflation rate So, r = .05 + .07 + (.05 x .07) = .1235 or 12.35%.
Annual Percentage Rate (APR)
The yearly uncompounded rate of interest
The __________ is a graphical representation of the term structure of interest rates.
The yield curve is a graphical representation of the term structure of interest rates. A yield curve is constructed from U.S. Treasury securities of differing maturities and plots yield on the y-axis and time to maturity on the x-axis. The resulting line that shows this relationship is known as the yield curve and it is typically upward sloping and to the right (normal yield curve). A time line is a tool used in finance that plots the amount and timing of a project's cash flows. Opportunity costs and real interest rates are not often graphed.
Differences in borrowing rates can generally be explained by the level of risk of the investment or loan and by the length of the investment or loan.
True
The number of periods for a consumer loan (n) is equal to the ________.
number of years times compounding periods per year
Nominal interest rates are the sum of two major components. These components are ________.
the real interest rate and expected inflation