Chapter 2 Interest Rates and Rates of Return Reading Notes Pages 21 29 The Interest Rate Present Value and Future Value Why Do Lenders Charge Interest on Loans Interest rate has to cover the opportunity cost of supplying credit Example You make a 1 000 loan to a friend who promises to pay you back in one year Three key facts you need to take into account when deciding how much interest to charge him 1 by the time your friend pays you back prices are likely to have risen so you will be able to but fewer goods and services than you could have if you had spent the money rather than lending it 2 your friend might not pay you back in other words he might default on the loan 3 during the period of the loan your friend has use of your money and you don t if he uses your money to buy a new computer he gets use of the computer for the whole year while you wait for him to pay your money back Think of the interest you can charge on a loan as being the result of Compensation for in ation Compensation for default risk the chance that the borrower will not pay you back the loan Compensation for the opportunity cost of waiting to spend your money Most nancial transactions involve payments in the future Examples When you take out a car loan you promise to make a payment every month until the car is paid o When you buy a bond issued by GE GE promises to pay you interest every year until the bond matures Say you need to borrow 15 000 from your bank to buy a car Consider two loans Loan A which requires you to pay 366 19 per month for 48 months Loan B which requires you to pay 318 71 per month for 60 months Which loan do you prefer Loan A has a higher monthly rate but lower interest rate 8 Loan B in vice versa 10 Suppose you deposit 1 000 in a bank certi cate of deposit CD that pays an interest rate of 5 What will be the future value of this investment Future value refers to the value at some future time of an investment made today In one year you will receive back your 1 000 principal which is the amount invested or borrowed and 5 interest on your 1 000 or 1 000 1 000 X 0 05 1 050 OR 1 000 X 1 0 05 1 050 If i the interest rate Principal the amount of your investment your original 1 000 FV the future value what your 1 000 will have grown to in one year then we can rewrite the expression as Principal X 1 i FVv1 Most Financial Transactions Involve Payments in the Future Compounding and Discounting Compounding for More Than One Period v1 subscript 1 after one year An Example of Discounting Suppose after one year you decide to reinvest in or roll over your CD for another year If you reinvest your 1 050 for a second year you will not only earn interest on your original 1 000 but also on the 50 in interest you earned the rst year Economist refer to this process of earning interest on interest as savings accumulate over time as compounding Compounding interest is an important component of the total amount you earn on any investment We can calculate the FV after two years of your initial investment Amount you earned after one year X Compounding during the second year FV after 2 years OR Principal X 1 0 05 2 FVv2 Example 1 000 X 1 0 05 X 1 0 05 1 102 50 OR 1 000 X 1 0 05 2 1 102 50 General function Principal X 1 i n FVvn Present value the value today of funds that will be received in the future Key Point funds in the future are worth less than funds in the present so funds in the future have to be reduced or discounted to nd their present value Time value of money the way that the value of a payment changes depending on when the payment is received Key Points 1 dollars in the future will usually buy less than dollars can today 2 dollars that are promised to be paid in the future may not actually be received 3 there is an opportunity cost in waiting to receive a payment because you cannot get the bene ts of the goods and services you could have bought if you had the money today To calculate present value we need to discount the value of funds we will not receive until the future Discounting is the process of nding the present value of funds that will be received in the future 1 000 1 050 1 0 05 OR PV FVv1 1 i General function PV FVvn 1 i n The larger the interest rate the smaller the present value Discounting and the Price of Financial Assets Discounting helps us compare the values of di erent nancial assets by giving us a means of determining the present value of payments to be received at di erent times in the future the price of nancial assets
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