Econ 101 1st Edition Exam 1 Study Guide Lectures 1 12 2 1 Time Value of Money Future Value and Compound Interest I Future Value a The value of a payment or a stream of payments at a future point in time II Compound Interest a Interest earned on interest III Simple Interest a Interest paid only on initial investment IV Ex a You have 100 invested in a bank account at an interest rate of 5 per year b After 1 year i Interest earned interest rate x initial principal ii Interest earned 05 x 100 5 iii Value of investment 1 100 5 105 iv Future value 1 100x 1 05 105 c After 2 years i Interest in year 2 05x 105 5 25 ii Value of Investment 1 105 5 25 110 25 iii Future Value 1 100x 1 05 2 110 25 2 2 Time Value of Money Present Value I II Present Value a The value today of a cash flow to be received in the future b Present Value for n periods Future value after n periods 1 r n Ex a How much do we need to invest now in order to obtain 105 at the end of the year i Future value 100x 1x 05 105 ii Present value 105 1 05 100 b How much do we need to invest now in order to obtain 110 25 at the end of the 2nd year i Future value 100x1 052 110 25 ii Present value 110 25 1 052 100 2 3 Time Value of Money Equation for Future and Present Value I II III IV V VI FV PV x 1 r n FV a Future value of an investment PV a Present value of an investment r i y on calculator a Interest rate per period n a Number of periods PV FV 1 r n 2 4 Time Value of Money Compounding More Frequently than Annually I Semiannual Compounding a You have 100 invested in a bank account for 1 year at an interest rate of 10 compounded semiannually After 1 year II III i FV 100 x 1 10 2 2x1 110 25 ii You put 2 for n because since it is semiannually you receive interest twice iii Interest on top of interest Quarterly Compounding a You have 100 invested in a bank account for 2 years at an interest rate of 10 compounded quarterly i Interest rate per year 10 ii Interest rate per quarter 10 4 2 5 iii Number of years 2 iv Number of periods quarters 8 1 FV 100 x 1 025 8 121 84 Compounding in General a FV PV x 1 r m m x n b m i The number of times compounding occurs in a year c Semiannual compounding m 2 d Quarterly compounding m 4 e Monthly compounding m 12 f Weekly compounding m 52 g Daily compounding m 365 h Continuous compounding FV PV x er 2 5 Time Value of Money Effective Annual Rate EAR vs Annual Percentage Rate APR I II III Annual Percentage Rate APR a The stated annual rate calculated by multiplying the periodic rate by the number of periods in one year b APR monthly rate x 12 Effective Annual Rate EAR a The annual rate of interest actually paid or earned reflecting impact of compounding frequency b EAR 1 APR m m 1 c EARcontinuous compounding eAPR 1 Ex a Suppose the interest rate on your credit card is 1 per month and you keep a 100 balance on the card for a year i Amount to be paid 100 x 1 01 12 112 68 b What if the interest rate on the credit card is 12 68 per year i Amount to be paid 100 x 1 1268 112 68 c 1 per month interest has an Effective Annual Rate EAR of 12 68 i 1 EAR 1 monthly rate 12 2 6 Time Value of Money Perpetuity and Annuity Due I II Perpetuity a A constant stream of cash flows that continues forever i PV PMT r b Ex i Consider a preferred stock with no maturity and promised annual payments of 400 million If the required rate of return is 10 what is its price 1 PV 400 million 01 4 billion Annuity due a An annuity for which cash flows occur at the beginning of each period i For these problems switch calculator to BEGIN mode Example Annuity Car Loan I II III IV V You want to buy a 20 000 car obtain a 5 year car loan and make a 5 000 down payment The loan requires you to make monthly payments The dealer offers you two choices a Low interest credit 3 b 1 000 discount and high interest credit 6 i Which one has lower monthly payments Choice 1 a Number of periods 5x12 60 months b Interest rate per period 3 12 25 c Amount borrowed 20 000 5 000 15 000 Choice 2 a Number of periods 5x12 60 months b Interest rate per periods 6 12 5 c Amount borrowed 20 000 5 000 1 000 14 000 Results a PMT Choice 1 269 53 b PMT Choice 2 270 65 Example Annuity Saving for a Down Payment I II You have just landed a job and are going to start saving for a down payment on a house You want to save 20 percent of the purchase price and then borrow the rest from a bank You have an investment that pays 10 APR Houses that you like and can afford currently cost 100 000 Real estate has been appreciating in price a 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 five years from today a The cost of the house in 5 years i 100 000 x 1 05 5 127 628 20 b Down payment required in 5 years i 20 x 127 628 20 25 525 64