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by: Gail Notetaker

Ch_4_Future_Value__Present_Value__and_Interest_Rates.pdf ECO4223

Marketplace > Florida Atlantic University > Economics > ECO4223 > Ch_4_Future_Value__Present_Value__and_Interest_Rates pdf
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Present and Future Values and Interest Rates
Money and Banking
Rupert Rhodd
Class Notes
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This 5 page Class Notes was uploaded by Gail Notetaker on Saturday September 3, 2016. The Class Notes belongs to ECO4223 at Florida Atlantic University taught by Rupert Rhodd in Fall 2016. Since its upload, it has received 3 views. For similar materials see Money and Banking in Economics at Florida Atlantic University.


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Date Created: 09/03/16
Money & Banking – ECO4223          09­03­16 Chapter 4 – Future Value, Present Value, and Interest Rates ­ Investment in future: o Not certain o Involves inflation ­ Credit: method for allocating resources; when someone borrows to cover needs (helps create  demand for goods/services, which requires companies to hire people = allocate resources) ­ Interest rates: price of resource allocation/credit; payment for lending/loaning o Connect present & future o Provide incentive for loaning (earn for letting someone borrow now) o Give the cost for borrowing in present and repaying in the future ­ Present Value: today’s value of a payment to be made later ­ Future Value: a future date’s value of a loan (for example) to be fully repaid on that date ­ Calculating FV o One year: FV = PV + PV (i) = PV (1 + i) o i.e. $1000 @ 10%; FV = 1000 (1 + .10) = 1000 (1.1) = $1100 o  Compound interest   = interest on interest rates o FV = FV = Pn (1 + i) n  N = periods 2  o i.e. $1000 @ 10%; FV  = 2000 (1 + .10) = $1210 m n o Monthly compounded interest: FV = P (1 + i )  P = PV = Principal  I = Monthly interest  n = # of months ­ Calculating PV FV o PV= n (1+i ) o PV higher if  FV is higher  Shorter time period on loan  Lower interest rates ­ Internal Rate of Return  o As long as IRR > interest rate paid on loan, investment should take place ­ Bonds: fixed interest ceiling assets; promise to make series of payments in future (dates  specific) o Coupon bond:  Most common kind of bond  Coupon payments: annual payments  Coupon rate: interest rate  Maturity date: date at which loan is repaid completely  Principal/Face value: final payment F o P= n (+i ) o i.e. P = $100, maturity = n years = 30, I = 6% F  P=100= 30  = (1.06)^30 (100) = F = $574.35 (1+.06 ) ­ Real and Nominal Interest Rates o Fisher Equation: i = r + π o Real interest rate = nominal interest rate – inflation  Money & Banking – ECO4223          09­03­16 Chapter 5 – Understanding Risk - Risk: 1. Can be measured  2. Caused by uncertainty 3. Deals with paying off an investment 4. Refers to an investment(s) 5. Needs to be assessed using timeline 6. Needs to be compared to a standard o Measuring Risk:   Probability: how likely something is to occur; number between 0 and 1  May be referred to as frequencies  i.e. Investment of $1000;   Possible outcomes:  o Stock value increases by $400 o Stock value decreases by $300 o Assume P’s is 0.5  Expected value: most likely outcome; mean***  Variance (financial risk) and Standard deviation (sq. root of variance) o **The higher the standard deviation, the greater the risk  Value at Risk (VaR): Worst possible loss at given probability over a  time period ***Image used from text/PPT***  o Sources of Risk: 1. Idiosyncratic/unique risks: only affects small population 2. Systemic/Economy­wide risks: affect ENTIRE population o Risk Diversification: holding multiple risks simultaneously  Methods for doing so:   Hedging: hold investments with “opposing risks” (text)  Spreading Risk: hold investments which have unrelated payoffs - Risk free asset: outcome is certain (associated with risk free rate of return) Money & Banking – ECO4223          09­03­16 Chapter 6 – Bonds, Bond Prices, and the Determination of Interest Rates ­ Bonds first introduced by Alexander Hamilton (first Secretary of US Treasury) o Used to consolidate debt from Revolutionary War o Invented by the Dutch, also used by British to cover government activities ­ Bond prices: what someone is willing to pay for a bond ­ Types of bonds: 1. Zero­coupon bond/Discount bond: a. Single payment (no coupon) b. i.e. US Treasury bill c. Breakdown of price: i.e. $1000 bond sells for $960, $40 = interest d. Price falls when interest rates go up Facevalue e. Equation:  Price= (+i ) 2. Fixed­payment loan: a. Involves stable payments  b. i.e. mortgage loan, car laon  c. Price of FP loan: sum of present value of payments Price= FV + FV +…+ FV d. Equation:  (+i ) (1+i ) (+i ) 3. Coupon bond:  a. Coupon/interest payments in addition to repayment of principal when the bond  matures b. i.e. US Treasury bonds, corporate bonds CouponPayments CPs CPs FV c. Price = PCB  ( 1+i ) + 1+i )+…+ (1+i ))+ 1+i ) 4. Consols/Perpetuities: a. Similar to coupon bonds, but payments are made “forever” b. Borrower only pays interest of the loan, and does not end up paying back the  principal c. i.e. Sold by US government in 1900, but all have been bought back YearlyCoupon Payment d. Price: PConsul  ( ) i ­ Bond yields: same definition as interest rate; the terms are used interchangeably o Yield to Maturity: payment received by bondholders when they hold it to its maturity  date $3 $100 o Price of 1yr 3% coupon bond =  (1+i) (1+i)


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