FINANC 3000 1st Edition Lecture 7 Outline of Last Lecture I. Future Value- Multiple Cash FlowsII. Future Value- Level Cash FlowsIII. The Cost of WaitingIV. Present Value- Multiple Cash FlowsV. Present Value- Level Cash FlowsVI. PerpetuityOutline of Current Lecture I. Compounding FrequencyII. EAR vs. APRIII. Loan AmortizationIV. 6 Months of “Free” FinancingV. Saving For a Down PaymentCurrent LectureCompounding Frequency- In finance we use compound interest- There are alternatives to annual compoundingo Many corporate and government bonds pay interest twice a year and have semiannual compoundingo Most mortgage loans and auto loans have monthly payments and thus monthly compoundingo The limiting case is continuous compounding- Works for annuity payments as well- Ex.o Instead of a total contribution of $4500 per year for 40 years, you are able to contribute monthly. Given your expected 7 percent per year investment return, how much money can you expect in your retirement account?These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. FVA40 = $375 x {[1+(0.07/12)]^460}-1}/(0.07/12)- =$375 x 2624.8135o =$984,305.02EARs and APRs- Quoted, or nominal rate called annual percentage rate (APR)o Legally required to be disclosedo The interest rate per period times the number of periods per year- Rate that incorporate compounding called effective annual rate (EAR)o An interest rate that reflects annualizing with compounding figured in - Relationship between APR and EAR:o EAR = {[1+(APR/m)]^m}-1- Ex.o As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 16 percent APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 15.5 percent APR and compounds weekly. Which card has a lower effective annual rate? EAR = {[1+(0.16/12)]^12}-1- =0.1732, or 17.23% EAR = {[1+(0.155/52)]^52}-1- =0.1674, or 16.74%Annuity Loans – Interest Rate- No easy formula- Compares implied interest rate- Allows easy comparison between two different investments- Allows to find required rate of returnFinding Payments on an Amortized loan- When amount of loan and interest rate is unknown, need to find amount of payment- A loan structured for annuity payment to completely pay off the debt – amortized loan- Rearrange PV of annuity formula to solve for paymento- Ex.o After you graduate and get your first job you’d like to realize your dream of owning Corvette. You find out the MSRP for it is $49,600 and your bank is willing to loan you this money at a 7% interest rate. You want to pay back the loan in 5 years. With now down payment, how much will your payments be? N = 5 x 12=60, I/Y = 7/12 = 0.58, PV = 49,600- PMT = -982.136 Months of “Free” Financing- The local car dealer is offering to let you drive away today in a $25,000 car if you agree to make 36 monthly payments of $806.68, the first payment due 6 months from today. What is the cash value of this offer of 6 months of “free” financing? The interest rate is 10% APR.o The PV of 36 monthly payments of $806.68 WITH THE FIRST PAYMENT IN ONE MONTH is $25,000.o The PV of $25,000 5 months from now is $23,983.88o This is $1,016.12 less than $25,000Saving for a Down Payment- You have just landed a job and are going to start saving for a down payment on a house. You want to save 20% of the purchase price and then borrow the rest from the bank.- You have an investment that pays 10% APR. Houses that you like and can afford currentlycost $100,000. Real estate has been appreciating in price at 5% per year and you expect this trend to continue.- How much should you save every month in order to have a down payment saved 5 yearsfrom today?o First we estimate that in 5 years, a house that costs $100,000 today will cost $127,628.16 N = 5, I/Y = 5, PV = -$100,000, PMT = 0- FV = $127,628.16o Next we estimate the monthly payment required to have $25,525.63 in 60 months. N = 60, I/Y = 10, PV = 0, PMT = -$329.63- FV = $25, 525.63 = 0.20 x $127,