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Week 6 Interest rates

by: Monica Garcia

Week 6 Interest rates

Marketplace > University of North Texas > > Week 6 Interest rates
Monica Garcia
GPA 3.2
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Interests rates
Finance 3779
Class Notes
Math, finance




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This 4 page Class Notes was uploaded by Monica Garcia on Sunday October 9, 2016. The Class Notes belongs to at University of North Texas taught by in Fall 2016. Since its upload, it has received 13 views.


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Date Created: 10/09/16
Effective Annual Rate: EAR  Example: with an ear of 5% a $100 investment grows to: o $100* (1+r)^2= $105 o Adjust the discount rate to different time periods, aka raising the interest rate factor (1+r). o Turning that one rate into different time periods  Ex: You make 5% per year, how much do you make every half year  1 year= (1+r)^1  6 months = (1+r)^.5  1 month = (1+r)^(1/12) o Equivalent n- period discount rate = (1+r)^n-1  When computing present or future values, you should adjust the discount rate to match the time period of the cash flows  If they don’t specify the time period of the rate than it is a yearlong rate o EX Problem:  Suppose your bank account pays interest monthly with an effective annual rate of 6%. What amount of interest will you earn each month?  (1+6%)^(1/12)- 1 =.49% How much should we deposit to end up with $100000 in 10 years. Payments will be monthly. Asking for monthly annuity. Insert into calculator: FV=100000 I=.49 (if you don’t round its technically .4868) N=10*12 (times 12 because its MONTHLY payments) PV=0 PMT=? Answer: $615.47 per month  The timing in the annuity formula must be consistent for all of the inputs. In other words if its monthly, all rates must be calculated in monthly payments, same thing for annual.  Annual Percentage Rates (APR) o Indicates the amount of interest earned in one year without the effect of compounding.  Simple interest rate: interest earned without the effect of compounding o Does not reflect the true amount you will earn over one year, it cannot be used as a discount rate o It’s a way of equating the actual interest earned each compounding period:  Interest rate per compounding period= APR/m  M= number of compounding periods per year  Ex: The difference between EAR and APR  EAR=6%--> monthly rate .49%  APR=6%  6%/12  there’s no compounding so APR is the rate divided by the compounding period. o Financial institutions have an obligation to tell you the APR not the EAR (the real costs)  Converting APR to an EAR o 1+EAR=(1+(APR/m))^m o M can be  Semi-annual=2  Quarter=4  Monthly=12  Daily= 365  Annual=1  Weekly=52S o Two steps  Convert APR to EAR 1+EAR=(1+(APR/m))^m  EAR to time period. (1+r)^n-1 Discount Rates/Loans  Compute loan payments. Consider the time line for a $30000 car loan with these terms: 6.75% APR for 60 months o Using the calculator o I/r=6.75%/12 Since everything is monthly and it’s APR you can just divide by 12 o N=60 months o Pv= $30,000 o FV=0 o Pmt= ? 5.2 Application: Discount and Loans  Computing Loan Payments  A lot of the time for these problems we are trying to figure out the RATE. Thus, it takes multiple steps to figure out this rate and this is where the difficulty of these problems occur. 5.3 What are the Determinants of Interest Rates  Inflation and Real Versus Nominal Rates o Nominal Interest Rates  The rate at which your money will grow if invested for a certain period  Any rate you get from the bank, car dealer, school, internet, wall street etc.  Not the real rate o Real interest rate  The rate of growth of your purchasing power, after adjusting for inflation.  Inflation- price is much higher (positive inflation)  Real measures the real growth o Inflation and real versus nominal rates  Growth in Purchasing Power=1+Real Rate= (1+Nominal rate)/ (1+ Inflation rate)  =Growth of Money/ Growth of Prices  Real Rate= (Nominal Rate-Inflation rate)/(1+inflation rate) = nominal rate – inflation rate  The Yield Curve and Discount rates o Term Structure  The relationship between the investment term and the interest rate  The longer you invest the more riskier or higher the interest rate o Yield Curve  A plot of bond yields as a function of the bonds’ maturity date o Risk-free Interest Rate  The interest rate at which money can be borrowed or lent without risk over a given period.  No firm can promise you that there will be no risks. o a risk-free cash flow of Cn received in n years has the PV  PV= (Cn)/(1+rn)^n where rn=the risk-free interest rate for an n- year term.  Interest Rate Determination o Federal Funds Rate  The overnight loan rate charged by banks with excess reserves at a federal reserve bnk to banks that need additional funds to meet reserve requirements  This is the private market, you do not use this rate  Yield Curve shapes o Normal- what we should expect at any point of time o Steep- when economy is recovering o Inverted-short-term don’t see very often Opportunity Cost of Capital  The best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted.


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