FIN 3100: Exam 2

Assume you just bought a new boat and now have a boat loan to repay. The amount of the principal is $68,000, the loan is at 6.75% APR, and the monthly payments are spread out over 7 years. What is the monthly loan payment?

$1,018 ---> Find the ordinary annuity - PV = PMT [ 1- (1 / (1+r)^n ) / r ] n = 7 years x 12 months = 84 months r = APR/12 months = 6.75% / 12 = 0.005625 68,000 = PMT [ 1 - (1 / (1 + 0.005625)^84 ) / .005625 ] PMT = 1,018

Your parents have an investment portfolio of $450,000, and they wish to take out cash flows of $60,000 per year as an ordinary annuity. How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%?

9.35 years --> PV = PMT [ 1- (1 / (1+r)^n ) / r ] 450,000 = 60,000 [ 1 - ( 1 + 0.0450)^n / .0450 ] 1/1.045^n = 0.6625 n = ln(1/0.6625) / ln( 1 + 0.0450) n = 9.35

A bond may be issued by __________.

All of these (companies, state governments, the federal government)

When quoting rates on loans, the "Truth in Lending Law" requires banks 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. (T/F)

TRUE

Suppose you deposit money in a certificate of deposit (CD) at a bank. Which of the following statements is TRUE?

The bank is technically renting money from you with a promise to repay that money with interest

Which of the following is NOT an example of annuity cash flows?

The grocery bill that changes every week

The "Truth in Savings Law" requires banks to advertise their rates on investments such as CDs and savings accounts as annual percentage yields (APY). (T/F)

TRUE

Five years ago, Clean Energy Corp issued an 10% coupon per year (paid semi-annually), 15-year, AA-rated bond at its par value of $1,000. Currently, the annual yield to maturity (APR) on these bonds is 8%. What is the current price per bond?

$1,135.90 --> bond value = PMT [ 1 - ( 1 / (1 + r)^n ) / r ] + [ face value / (1 + r)^n # of periods = (15 years - 5 years already passed) x 2 = 20 periods rate = 8% / 2 = 4% coupon = coupon % x par value = 10% x 1,000 = 100 annually --> 100/2 = 50 for semi-annually bond value = 50 [ 1 / (1 + 0.04)^20 / 0.04 ] + [ 1,000 / (1 + 0.04)^20 bond value = 1,135.90

Assume that Ray is 38 years old and has 27 years for saving until he retires. He expects an APR of 7.5% on his investments. How much does he need to save if he puts money away monthly in equal end-of-the-month amounts to achieve a future value of $1,200,000 dollars in 27 years' time?

$1,148.81 ---> Monthly rate = 7.5%/12 = 0.625% = 0.00625 # of months = 27 x 12 = 324 1,200,000 = PMT [ ( (1 +r)^n - 1 ) / r ] 1,200,000 = PMT [ (1+ 0.00625)^324 - 1 / 0.00625 ] PMT = 1,148.81

What if Jennifer were to invest $2,750 today, compounded semi-annually, with an annual percentage rate of 5.25%. What amount of interest will Jennifer have earned in one year?

$146.27 ---> rate = 5.25% / 2 = 2.625% # of periods = 1 year x 2 = 2 periods FV = PV ( 1 + r)^n FV = 2,750 (1 + 0.02625)^2 = 2,896.27 interest earned = 2,896.27 - 2,750 = 146.27

Lily invested $10,000 five years ago with an insurance company that has paid her 4% APR, compounded semi-annually. How much did Lily earn over the 5 years?

$2,189.94 --> FV = PV (1 + r)^n # of periods = 5 years x 2 = 10 periods r = 4% / 2 = 2% FV = 10,000 (1 + 0.02)^10 = 12,189.94 interest earned = 10,000 - 12,189.94 = 2,189.94

The Canadian government has once again decided to issue a consol ( a bond with a never ending interest rate and no maturity date). The bond will pay $100 in interest each year (at the end of the year), but it will never return the principal. The current discount rate for Canadian government bonds is 4%. What should this consol bond sell for in the market?

$2,500 ---> perpetuity PV = PMT / r PV = 100 / 0.04 = 2,500

Flashstream Productions Inc. is issuing a zero-coupon bond that will have a maturity of 50 years. The bond's par value is $1,000, and the current yield on similar bonds is 7.5%. What is the expected price of this bond, using the semiannual convention (i.e., assuming semiannual compounding)

$25.19 ---> Zero-Coupon Bond $ = FV / (1 + r) ^n *you will need to double the maturity & the divide the % b/c it is semi-annual (meaning, 2x per year) Zero- Coupon Bond $ = 1,000 / (1 + .0375)^100 = 25.19

What is the future value at the end of year four of an ordinary annuity cash flow of $6,000 per year at an interest rate of 12.00% per year?

$28,675.97 ---> FV ordinary annuity = PMT [ (1+r)^n - 1 / r ] FV = 6,000 [ (1 + 0.12)^4 -1 / 0.12 ] FV = 28,675.97

Plimpton has an annuity due that pays $800 per year for 11 years. What is the present value of the cash flows if they are discounted at an annual rate of 7.50%

$6,291.26 ---> PV = PMT [ (1 - ( 1 / (1 + r)^n) / r ] x (1 + r)^1 PV = 800 [ (1 - (1 - (1 + .075)^11) / .075 ] x (1 + .075)^1 PV = 6291.26

Twenty years ago Bison Enterprises Inc. issued 30-year 9% annual coupon bonds with a $1,000 face value each. Since then, interest rates in general have risen and the yield to maturity on the firm's bonds is now 11%. Given this information, what is the price today for a bond from this issue?

$8,882.22 ---> bond value = PMT [ 1 - ( 1 / (1 + r)^n ) / r ] + [ FV / (1 + r)^n coupon = 1,000 x 9% = 90 r = 11% bond value = 90 [ 1 - ( 1 / (1 + .11)^30) / .11 ] + [1000 / (1 + .11)^30 bond value =

Suppose you postpone consumption and invest at 14% when inflation is 2%. What is the approximate real rate of your reward for saving?

12% (14% - 2% = 12%)

The effective annual rate (EAR) is 20% with daily compounding. What is the stated rate (APR)?

18.24% APR = m [ (1 + EAR) ^1/m - 1 ] APR = 365 [ (1 + 0.20) ^1/365 - 1 ] = 0.1824 APR = 18.24%

You are comparing 2 separate investments. Each one is for a period of 10 years and pays $2,500 a year. You require a 10% return on these investments. Investment A pays at the beginning of each year and Investment b pays at the end of each year. Given this situation, which one of the following statements is accurate.

Investment A has both a higher PV and a higher FV than Investment B

MacroMedia Inc. $1,000 par value bonds are selling for $832. Which of the following statements is TRUE?

None of these are true

What is the EAR if the APR is 10.52% and compounding is daily?

Slightly above 11.09% --> EAR = [ 1 + APR/m]^m - 1 EAR = [ 1 + 0.1052/365]^365 - 1 EAR = 0.1109 --> 11.09%

Which of the following is NOT true with regard to an amortization table?

The remaining principal balance at the end of a payment period is equal to the beginning-of-the-period principal less the total payment.

A finite series of equal payments that occur at regular intervals is called a(n) __________.

annuity

The __________ is the regular interest payment of the bond.

coupon

An annuity is a series of __________.

equal cash payments at regular intervals across time

When real property is used as collateral for a bond, it is termed a(n) __________.

mortgaged security

Theresa borrows $800 today in exchange for one payment of $1,000 five years from now. This is an example of a(n):

pure discount loan

When a company is in financial difficulty and cannot fully pay all of its creditors, the first lenders to be paid are the __________.

senior debtholders

As the rating of a bond increases ( for example, from A, to AA, to AAA), it generally means that __________.

the credit rating increases, the default risk decreases, and the required rate of return decreases

The __________ is a market derived interest rate used to discount the future cash flows of the bond.

yield to maturity