FINANCIAL
Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 5.7%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?
(1+0.05/4)^4 -1 =0.0509 -----5.09 (1+0.057/1)^1 -1 =0.057 ---- 5.7 5.7-5.09= 0.61
Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 3.1%, how much is the bond worth today?
1000/(1+0.031)^10 =$736.91
You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $280,000?
=NPER(7%/12,-3000,,280000) = 75 months Rate: 7%/12 Pmt: -3,000 Pv: Fv: 280,000 Type:
Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $92,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?
=RATE Nper= 12 Pmt= 15,000 Pv= -92,000 Fv= 0 Type= 1 =0.154813448 ---- 15.48%
Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?
A bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
You plan to invest in securities that pay 11.6%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?
A=P(1+r/100)^n A=future value P=present value r=rate of interest n=time period. 9,140.20=5,000*(1.116)^n (9,140.20/5,000)=(1.116)^n Taking log on both sides; log (9,140.20/5,000)=n*log (1.116) n=log (9,140.20/5,000)/log (1.116) =5.50 years
Which of the following bank accounts has the highest effective annual return?
An account that pays 8% nominal interest with daily (365-day) compounding.
Which of the following statements is CORRECT? a.If the maturity risk premium (MRP) is greater than zero, then the yield curve must have an upward slope. b.The yield curve can never be downward sloping. c.Because long-term bonds are riskier than short-term bonds, yields on long-term Treasury bonds will always be higher than yields on short-term T-bonds. d.If the maturity risk premium (MRP) equals zero, the yield curve must be flat. e.If inflation is expected to increase in the future, and if the maturity risk premium (MRP) is greater than zero, then the Treasury yield curve will have an upward slope.
E
Suppose you deposited $8,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
FV=PV*[(1+Interest Rate)^# of periods] =8000*[(1+0.00014583)^240]= =$8,284.93
If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.
False
Since yield curves are based on a real risk-free rate plus the expected rate of inflation, at any given time there can be only one yield curve, and it applies to both corporate and Treasury securities.
False
The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.
False
Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.
False
Assume that inflation is expected to decline steadily in the future, but that the real risk-free rate, r*, will remain constant. Which of the following statements is CORRECT, other things held constant?
If the pure expectations theory holds, the Treasury yield curve must be downward sloping.
If the pure expectations theory of the term structure is correct, which of the following statements would be CORRECT?
Interest rate (price) risk is higher on long-term bonds, but reinvestment rate risk is higher on short-term bonds.
An upward-sloping yield curve is often call a "normal" yield curve, while a downward-sloping yield curve is called "abnormal."
TRUE
If investors expect a zero rate of inflation, then the nominal rate of return on a very short-term U.S. Treasury bond should be equal to the real risk-free rate, r*.
TRUE
The "yield curve" shows the relationship between bonds' maturities and their yields.
TRUE
The real risk-free rate of interest is expected to remain constant at 3% for the foreseeable future. However, inflation is expected to increase steadily over the next 30 years, so the Treasury yield curve has an upward slope. Assume that the pure expectations theory holds. You are also considering two corporate bonds, one with a 5-year maturity and one with a 10-year maturity. Both have the same default and liquidity risks. Given these assumptions, which of these statements is CORRECT?
The 10-year corporate bond must have a higher yield than the 5-year corporate bond.
Assuming that the term structure of interest rates is determined as posited by the pure expectations theory, which of the following statements is CORRECT?
The maturity risk premium is assumed to be zero.
A time line is meaningful even if all cash flows do not occur annually.
True
Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 2.80%. What rate of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
r = r* + IP + DRP + LP + MRP r = 2.50% + 2.80% = 5.30%
Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?
r= (1+i/n) ^n - 1 r= (1+0.065/12)^12 -1 = 0.06697 =6.697 6.697-6.2= 0.497 =-50%
