Solving Simple Interest Problems using Systems of Equations The simple interest I earned after one year on a deposit of principal P in an account earning interest at an annual rate r is given by
(Notice that this is the Basic Percent Equation with percent r, base P and amount I.)
The problems below involve investing money in two different accounts, each paying annual simple interest at a different rate. For each problem, write one equation in two variables expressing a relationship between the principals invested in the accounts, and another equation involving the interest earned. Solve the system of the two equations then use the solution to answer the question.
Example: A total of $8000 is deposited in two simple interest accounts. One one account, the annual simple interest rate is 5%, and on the second account, the annual simple interest rate is 6%. How much should be invested in each account so that the total annual interest earned is $450? Step 1: Use two variables to define two unknown quantities.
Let x represent the principal invested in the account paying 5% interest.
Let y represent the principal invested in the account paying 6% interest.
Step 2: Write an equation involving the principal invested in the two accounts. 8000
Step 3: Write an equation involving the interest earned from the two accounts. Since the interest earned from each account is given by the product of its interest rate and principal, we have
0.05
0.06
450
Step 4: Solve the system consisting of the equations from Steps 2 & 3.
Solution: (3000, 5000)
Step 5: Use the solution of the system to answer the question.
$3000 should be invested at 5% and $5000 should be invested at 6%.
Example: A sports foundation deposited a total of $24,000 into two simple interest accounts. The annual simple interest rate on one account is 7%. The annual simple interest rate on the second ...
...Interest Rates and Bond Valuation
Chapter 6 6.2 More on Bond Features
Securities issued by corporations are classified as equity securities and debt securities. A debt in very simple terms represents something that must be paid as a result of borrowing money, when corporations borrow money they make regular interest payments as well as paying the principal amount at the end of the period. There are three main differences between debt and equity, which are: Debt is not ownership; creditors don't have any say in the firm's decisions. Interest is taxable, but dividends are not tax deductible. Unpaid debt is a liability on the firm; if the firm goes bankrupt creditors can legally claim assets of the firm. Debt can result to financial failure, but this is not the case when equity is issued. Is it Debt or Equity? Sometimes it is unclear if what the firm is offering is a debt or equity security. The main purpose behind doing this is so that firms offer debts that are actually equity securities so that they can obtain tax benefits from debts and the bankruptcy benefits of equity. Debt holders are usually paid before equity holders. The rewards for owning a debt is fixed according to the loan's amount, but there is no limit to the available rewards that can be gained from owning equity, the higher the profit the bigger the interest amount. Longterm Debt: The Basics Even...
...Understanding the Term Structure of Interest Rates
Prepared for Fundamentals of Financial Management
Distributed
October 24, 2005
TABLE OF CONTENTS
List of Figures....................... ....................................... .....................iii
List of Abbreviations and Symbols............................. ..........................iv
Summary............................................................................. ...................5
Introduction.......................................... .................................................7
Understanding the Term Structure of Interest Rates ............. ...............8
Term Structure Puzzle................................................................8
The Yield Curve .8
The Expectations Theory 9
Visual Aids..............................................................................10
Conclusions ......... .............................. .............11
LIST OF FIGURES
Figure 1: Expected Yield Curve When Inflation Is Expected to Increase ..4
Figure 2: Expected Yield Curve When Inflation Is Expected to...
...return on debt of a project/firm
Always true.
Never true.
Sometimes true.
Question 3
(10 points) Moogle, Inc. is in the same business as Google, Inc., but has recently retired all its debt to become an allequity firm. Its return on equity has dropped from 12.25% to 10.60% as a result of this. Google, Inc. continues to have debt in its capital structure, and its debttoequity ratio is 30%. What is the return on assets of Google, Inc.(No more than two decimals in the percentageinterest rate, but do not enter the % sign.)
Answer for Question 3
Question 4
(10 points) Suppose CAPM holds, and the beta of the equity of your company is 2.00. The expected market risk premium (the difference between the expected market return and the riskfree rate) is 4.5% and the riskfree rate is 3.00%. Suppose the debttoequity ratio of your company is 20% and the market believes that the beta of your debt is 0.20. What is return on assets of your business? (No more than two decimals in the percentage interest rate, but do not enter the % sign.)
Answer for Question 4
Question 5
(10 points) You are planning on opening a consulting firm. You have projected yearly cash flows of $2 million starting next year (t = 1) with a growth rate of 3% over the foreseeable future thereafter. This endeavor will require a substantial investment and you will have to convince investors to provide you the capital to do so. You will invest some of your own money,...
...Question 2
You expect interest rates to decline over the next six months.
a. Given your interest outlook, state what kinds of bonds you want in your portfolio in terms of duration and explain your reasoning for this choice. (5 marks)
b. You must make a choice between the following three sets of noncallable bonds. For each set, select the bond that would be best for your portfolio given tour interest rate outlook and the consequent strategy set forth in part (a). In each case briefly discuss why you selected the bond. (15 marks)
  Maturity Coupon YTM 
Set 1: Bond A 15 years 10% 10% 
 Bond B 15 years 6% 8% 
Set 2: Bond C 15 years 6% 10% 
 Bond D 10 years 8% 10% 
Set 3: Bond E 12 years 12% 12% 
 Bond F 15 years 12% 8% 
Question 3
At the present time, you expect...
...wins? If not, who loses?
Introduction:
Players: Morgan Bank, Rabobank, and B.F. Goodrich, Salomon Brothers, Thrift Institutions and Saving Banks
Goodrich:
In early 1983, Goodrich needed $50 million to fund its ongoing financial needs. However, Goodrich was reluctant to borrow (short term debt) from its committed bank lines because of the following reasons:
1. It would lose substantial about of its remaining short term capital availability under its bank lines.
2. It would compromise its future flexibility by borrowing in the short term.
Instead, it wanted to borrow for an 8 year range (or longer) at a fixed rate.
However, since the general level of interest rates were pretty high, and Goodrich’s credit ratings had dropped from BBB to BBB. Goodrich believed that it would have to pay 13% interest for a 30 year corporate debenture.
Salomon Brothers had advised Goodrich that they could borrow in the US public debt market with a floating rate debt issue tied to the LIBOR, and then swap payments with Euro market bank that had raised funds in the fixedrate Eurobond market.
Note: The reason that Salomon were confident that this could be done is described as follows:
1. There was a recent deregulation of deposit markets had allowed deposit institutions to offer new variable rate money market deposit accounts.
2. As result of these new offerings large thrift institutions
Rabobank:
Rabobank had AAA debt ratings, and...
...w/ shifts in general level of int rates
zero couponpays no annual int but seels @ discount below par
junk bondhigh risk, high yield bond, used to finance mergers, leveraged buyouts
foreign debtdebt sold by foreign borrower but is denominated in currency of country in which issue is sold
eurodebtused to designate any debts sold in country other than the one whose currency it’s denominated
total ret = coupon (int) + cap gains yield (Chngprice)
original price
yield to maturityave rate of return earned on bond if it’s held to maturity
yield to call – avg rate of return earned on a bond if it’s held until first call date
semiannual compoundingbond pay $50 int every 6 months rather than 100 at the end of each year. Simple rate of int is 8% w/ semiannual compounding, value of bond when there are 14 years remaining –N=28 (14x2), I=4(8/2), INT=PMT=50(100/2),M=FV=1000, PV?1166.63
changes in bond value – whenever the going roate of int (rd)=coupon rate, a bond will sell @ its par
*an in int rates will cause price of outstanding bond to fall
*a in int rates will cause price to rise
*mkt value of a bond will always approach its par value as its maturity date approaches
bond yield=current(int)yield+cap gains yield
(INT/Vbeg) +VendVbeg/Vbeg
int rate reinvestment rate riskrisk that inc from bond portfolio will vary bc CF have to be reinvested @ current (lower) mkt rates
@ time bond is issued,...
...and Structure of Interest rates
P C Narayan
IIMB PCN BFMS L02
1
Loanable Funds theory
“Market interest Rate is
determined by the factors
that control the supply and
demand for loanable funds”
IIMB PCN BFMS L02
2
1
Demand for Loanable Funds
• Household demand for loanable funds
– As household income rises, so does installment debt
– Inverse relationship between demand for lonable funds
and interest rate
• Business demand for loanable funds
– Inverse relationship between demand for lonable funds
and interest rate
• Government demand for loanable funds
– Interest inelastic since borrowing to meet deficit
• Foreign demand for loanable funds
– Country A issues securities to investors of country B
• Total Demand for lonable funds Da =
Dh + Db + Dg + Df
IIMB PCN BFMS L02
3
Supply of Loanable Funds
• Household sector is the largest followed by
Government and Business (Sa)
• Directly proportional to interest rates
_______________________________________
In equilibrium, Da = Sa
• And the interest rate at this point is is known as
‘equilibrium interest rate’
• Change in demand or supply causes a change in
‘equilibrium interest rate’
IIMB PCN BFMS L02
4
2
Fisher Effect
• Offers an additional explanation to the loanable
funds theory
• Nominal Interest rate
– Compensates for reduced purchasing power
– Provides a premium for...
...Jamie wants to earn $500 in interest so she’ll have enough to buy a used car. She puts $2000 into an account that earns interest. How long will she need to leave her money in the account to earn $500 in interest? 
  
Question #2 
  A local bank is advertising that you can double your money in eight years if you invest with them. Suppose you have $1000 to invest. What interest rate is the bank offering? 


Try These 
 
     
Question #1 
  Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest. How much will be in Kelly’s account at the end of four years? 
 A. $127.50 
 B. $754.0425 
 C. $877.50 
 D. $1275 
    
Question #2 
  Randy wants to move his savings account to a new bank that pays a better interest rate of 3.5% so that he can earn $100 in interest faster than at his old bank. If he moves $800 to the new bank, how long will it take for him to earn the $100 in interest? 
 A. 3.57 years 
 B. 0.357 years 
 C. 0.28 years 

A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years....