Money and Banking Chapter 4 Interest Rates

Chapter Interest Rates CHAPTER OBJECTIVES By the end of this chapter , students should be able to . Define interest and explain its importance . Write and explain the present value formula . Write and explain the future value formula . Calculate present and future value for multiple periods with annual and more frequent compounding . Define and price major types of debt instruments including discount bonds , simple loans , fixed payment loans , and coupon bonds . Define yield to maturity and identify the types of financial instruments for which it is relatively easy to calculate . Explain why bond prices move inversely to market interest rates . Explain why some bond prices are more volatile than others . Define rate of return and explain how it differs from yield to maturity . 10 . Explain the difference between real and nominal interest rates . URL books , 50

The Interest of Interest LEARNING OBJECTIVE . What is interest and why is it important ?

Interest , the opportunity cost ofmoney , mysterious , but it warrants our careful consideration because ofits importance . Interest rates , money , are crucial ofthe prices , instruments like stocks and bonds , and general conditions , including economic growth . In fact , like your grades ! the probability of you landing a job upon graduation will depend in large part on prevailing interest rates . If rates are low , businesses will be more likely to borrow money , expand production , and hire you . If rates are high , businesses will be less likely to expand or to hire you . Without a job , you be forced to move back home . Best to pay attention then ! Interest can be thought of as the payment it takes to induce a lender to part with his , her , or its money for some period of time , be it a day , week , month , year , decade , or century . To make comparisons between those payments easier , interest is almost always expressed as an annual percentage rate , the number of dollars ( or other currency ) paid for the use of 100 per year . Several ways of measuring interest rates exist , but here you learn only yield to maturity , the method preferred by economists for its accuracy . The key is to learn to compare the value of money today , called present value ( represented here by the Variable and aka present discounted value or price ) to the value of money tomorrow , called future value ( represented here by the variable ) KEY TAKEAWAYS Interest is the opportunity cost of lending money or the price of borrowing it and can be thought of as the payment a borrower needs to induce him , her , or it to lend . Interest is important because it helps to determine the price of assets , especially financial assets , and to determine various variables , including aggregate output . URL books 61

Present and Future Value LEARNING OBJECTIVE . What are the formulas for present value and future value , and what types of questions do they help to answer ?

A moment should convince you that money today is always more than money tomorrow . If you don believe me , send me all of your money immediately . I return every cent of scout exactly one year . I wont hold my breath . You be foolish indeed to forgo food , clothes , housing , transportation , and entertainment for a year for no remuneration whatsoever . That why a dollar today is worth more than a dollar tomorrow . Another reason that a dollar today is worth more than a dollar tomorrow is that , in modern economies , for reasons discussed in Chapter 17 Monetary Policy Targets and Goals , prices tend to rise every year . So 100 tomorrow will buy fewer goods and services than 100 today will . We will discuss the impact of on interest rates more at the end of this chapter . For now , we consider only nominal interest rates , not real interest rates . But what if I told you that if you gave me 100 today , give you in a year ?

Most lenders would jump at that offer ( provided they thought I would pay as promised and not default ) but I wouldn offer it and neither would most borrowers . In fact , about 110 would be the most I be willing to give you in a year for 100 today . That an interest rate of 10 percent ( 100 or 10 ) which , as comedian Adam Sandler might say , is not too If we let the loan ride , as they say , capitalizing the interest or , in other words , paying interest on the interest every year , called annually compounding interest , your 100 investment would grow in value , as shown in Figure The fate of 100 invested at 10 , compounded annually . Figure ' URL books 52

10 11 12 14 15 16 18 19 20 The in the table are easily calculated by multiplying the previous years value by , representing the principal value and representing the interest rate expressed as a decimal . So 100 today ( year ) is , at 10 percent interest compounded annually , worth 110 in a year ( 100 ) 121 after two years ( 110 ) after three years ( 121 ) and so forth . The quick way to calculate this for any year is to use the following formula ( i ) where the future value ( the value of your investment in the future ) the present value ( the amount of your investment today ) i ) the future value factor ( aka the present value factor or discount factor in the equation below ) i interest rate ( for example , 25 , etc . number of terms ( here , years elsewhere days , months , quarters ) URL books ( 519 53

For 100 borrowed today at 10 percent compounded annually , in 100 years I owe you ( 100 ) Good luck collecting that one ! What if someone offers to pay you , say , in years ?

How much would you be willing to pay today for that ?

Clearly , something less than . Instead of taking a and expanding it via multiplication to determine an , here you must do the opposite , or in other words , reduce or discount an to a . You do so by dividing , as in the following formula ( nur ( Obviously , we cant solve this equation unless one of the two remaining variables is given . If the interest rate is given as percent , you would pay today for payable in years ( If it is 20 percent , you give only ( If it is percent , you would give ( Notice that as the interest rate rises ( falls ) ofthe ( rises ) In other words , the price payment ( some generically , a bond ) and the rate are inversely related . You can see this algebraically by noting that the i term is in the denominator , so as it gets larger , must get smaller ( holding constant , of course ) Economically this makes sense because a higher interest rate means a higher opportunity cost for money , so a sum payable in the future is worth less the more dear money is . If payment of the bond described just above were to be made in ten years instead of five , at percent interest per year , you pay ( Note here that , holding the interest rate ( and all other factors ) constant , you give less today for a payment further in the future ( That too makes good sense because you re without your money longer and need to be compensated for it by paying a lower price for the today . Stop and Think Box Congratulations , you just won the Powerball 100 million payable in million installments over 20 years ! Did you really win 100 million ?

Hint Calculate the of the payment with interest at percent . URL books No 20 100 , but the money payable next year and in subsequent years is not worth million today if interest rates are above , and they almost always are . For example , the last payment , with interest rates at percent compounded annually , has a of only , ooo , This is a great place to stop and drill until calculating present value and future value becomes second nature to you . Work through the following problems until it hurts . Then do them again , standing on your head or on one leg . EXERCISES For all questions in this set , interest compounds annually and there are no transaction fees , defaults , etc . On your seventieth birthday , you learn that your grandma , bless her soul , deposited for you on the day of your birth in a savings account bearing percent interest . How much is in the account ?

You won million in the lottery but unfortunately the money is payable in a year and you want to start spending it right away . If interest is at percent , how much can you receive today in exchange for that million in year ?

As a college freshman , you hoped to save to pimp your ride as a college graduation present to yourself . You put from your high school graduation haul in the bank at percent interest . Will you meet your goal ?

You won a scholarship for your senior year worth , but it is payable only after graduation , a year hence . If interest is at 15 percent , how much is your scholarship worth today ?

You determine that you need saved in order to retire comfortably . When you turn 25 , you inherit . If you invest that sum immediately at percent , can you retire at age 65 if you have no other savings ?

You own two bonds , each with a face , or payoff , value of . One falls due in exactly one year and the other in exactly three years . If interest is at percent , how much are those bonds worth today ?

What if interest to percent ?

To purchase a car , you borrowed from your brother . You offered to pay him percent interest and to repay the loan in exactly three years . How much will you owe your bro ?

As part of a lawsuit settlement , a major corporation offers you today or next year . Which do you choose if interest rates are percent ?

If they are percent ?

URL books 65 . Exactly 150 years ago , the government promised to pay a certain Indian tribe , or percent interest until it did so . Somehow , the account was unpaid . How much does the government owe the tribe for this promise ?

10 . As part of an insurance settlement , you are offered today or in five years . If the applicable interest rate is percent , which option do you choose ?

What if the interest rate is percent ?

KEY TAKEAWAYS The present value formula is ( i ) where present value , future value , interest rate , and number of periods . It answers questions like , How much would you pay today for at time in the future , given an interest rate and a compounding period . The future value formula is ( i ) It answers questions like , How much will invested today at some interest rate and compounding period be worth at time ?

Certain interest rates occasionally turn very slightly ( negative . The phenomenon is so rare and minor that it need not detain us here . sandler URL books 66 Compounding Periods LEARNING OBJECTIVE . If interest compounds other than annually , how does one calculate and ?

Interest does not always compound annually , as assumed in the problems already presented in this chapter . Sometimes it compounds quarterly , monthly , daily , even continuously . The more frequent the compounding period , the more valuable the bond or other instrument , all else constant . The mathematics remains the same ( though a little more difficult when compounding is continuous ) but you must be careful about what you plug into the equation for i and For example , invested at 12 percent for a year compounded annually would be worth ( But that same sum invested for the same term at the same rate of interest but compounded monthly would grow to ( because the interest paid each month is capitalized , earning interest at 12 percent . Note that we represent i as the interest paid per period ( 12 months in a year ) and as the number of periods ( 12 in a year 12 12 ) rather than the number of years . That same sum , and so forth with interest compounded quarterly ( times a year ) would grow to ( The differences among annual , monthly , and quarterly compounding here is fairly trivial , amounting to less than all told , but is important for bigger sums , higher interest rates , more frequent compounding periods , and longer terms . One million dollars at percent for a year compounded annually comes to ( while on the same terms compounded quarterly , it produces ( Ill take the latter sum over the former any day and invest the surplus in a very nice dinner and concert tickets . Likewise , 100 at 300 percent interest for years compounded annually becomes 100 ( Compounded quarterly , that 100 grows to 100 ( A mere at percent compounded annually for 100 years will be worth ( The same buck at the same interest compounded monthly swells in a century to ( This all makes good sense because interest is being received sooner than the end ofthe year and hence is more valuable because , as we know , money now is better than money later . Do a few exercises now to make sure you get it . EXERCISES URL books 67

For all questions in this set , interest compounds quarterly ( four times a year ) and there are no transaction fees , defaults , etc . On your seventieth birthday , you learn that your grandma , bless her soul , deposited for you on the day of your birth in a savings account bearing percent interest . How much is in the account ?

You won million in the lottery but unfortunately the money is payable in a year and you want to start spending it right away . If interest is at percent , how much can you receive today in exchange for that million in year ?

As a freshman , you hoped to save to pimp your ride as a college graduation present to yourself . You put from your high school graduation haul in the bank at percent interest . Will you meet your goal if you graduate in four years ?

You won a scholarship for your senior year worth , but it is payable only after graduation , a year hence . If interest is at 15 percent , how much is your scholarship worth today ?

EY TA Present and future value can be calculated for any compounding period using the same formulas presented in this chapter . Care must be taken , however , to ensure that the terms are adjusted appropriately . URL books 68 Pricing Debt Instruments LEARNING OBJECTIVE . What are debt instruments and how are they priced ?

Believe it or not , you are now equipped to calculate ofany debt instrument or contract provided you know the rate , compounding period , and the size and timing ofthe payments . Four major types of instruments that you are likely to encounter include discount coupon bonds , simple loans , loans , and coupon bonds . A discount bond ( aka a zero coupon bond or simply a zero ) makes only one payment , its face value on its maturity or redemption date , so its price is easily calculated using the present value formula . A simple loan is the name for a loan where the borrower repays the principal and interest at the end of the loan . Use the future value formula to calculate the sum due upon maturity . A loan ( aka a fully amortized loan ) is one in which the borrower periodically ( for example , weekly , bimonthly , monthly , quarterly , annually , etc . repays a portion of the principal along with the interest . With such loans , which include most auto loans and home mortgages , all payments are equal . There is no big balloon or principal payment at the end because the principal shrinks , slowly at first but more rapidly as the final payment grows nearer , as in Figure Sample mortgage . Principal borrowed Annual number of payments 12 Total number of payments 360 Annual interest rate 600 Regular monthly payment amount Figure Sample ' URL books 69

Today , such schedules are most easily created using specialized software , including Web sites like , or calculators . If you wanted to buy this mortgage ( in other words , if you wanted to purchase the right to receive the monthly repayments of ) from the original lender ( there are still secondary markets for mortgages , though they are less active than they were before the financial crisis that began in 2007 ) you simply sum the present value of each of the remaining monthly payments . Again , a computer is highly recommended here ! Finally , a coupon bond is because , in the past , owners of the bond received interest payments by clipping one of the coupons and remitting it to the borrower ( or its paying agent , usually a bank ) Figure Sample bond coupon , Melrose Railroad , 1860 , for example , is a coupon paid ( note the cancellation holes and stamp ) to satisfy six months interest on bond number 21 of the Melrose Railroad Company of Boston , Massachusetts , sometime on or after April , 1863 . Figure Michigan Central Railroad , percent bearer gold bond with coupons attached , 1902 is a par Value coupon bond issued in 1932 , with many of the coupons still attached ( on the right side of the ) Figure Sample bond coupon , Melrose Railroad , 1860 ' The Will the Bearer at the I ' in , mum , on the 13 ! til , for six months dated . 1360 . Courtesy Figure Central Railroad , percent bearer gold mud with coupons , 1902 URL books 71

! sun um ' Museum ofAmerican Finance Even if it no longer uses a physical coupon like those illustrated in Figure Sample bond coupon , Melrose Railroad , 1860 and Figure Michigan Central Railroad , percent bearer gold bond with coupons attached , 1902 , a coupon bond makes one or more interest payments periodically ( for example , monthly , quarterly , semiannually , annually , etc . until its maturity or redemption date , when the interest payment and all of the principal are paid . The sum of the present values of each future payment will give you the price . So we can calculate the price today of a face or par Value coupon bond that pays percent interest annually until its face value is redeemed ( its principal is repaid ) in exactly years if the market rate of interest is percent , percent , or any other percent for that matter , simply by summing the present Value of each payment URL books ( 61 ME 72

. This is the interest payment after the first year . The 500 is the coupon or interest payment , which is calculated by multiplying the bond face value , in this case , by the bond contractual rate of interest or coupon rate , in this case , percent . 500 . does look familiar , you didn do Exercise enough ! is the interest payment 500 plus the repayment ofthe bond face value . That adds up to . If you are wondering why the bond is worth less than its face value , the key is the difference between the contractual interest or coupon rate it pays , percent , and the market rate of interest , percent . Because the bond pays at a rate lower than the going market , people are not willing to pay as muchfor it , so its price sinks below par . By the same reasoning , people should be willing to pay more than the face value for this bond if interest rates sink below its coupon rate of percent . Indeed , when the market rate of interest is percent , its price is ( give or take a few pennies , depending on rounding ) If the market interest rate is exactly equal to the coupon rate , the bond will sell at its par value , in this case , Check it out ( 476 . 1905 ( URL books 73

( Calculating the price of a bond that makes quarterly payments over thirty years can become quite tedious because , by the method shown above , that would entail calculating the of 120 ( 30 years times payments a year ) payments . Until not too long ago , people used special bond tables to help them make the calculations more quickly . Today , to speed things up and depending on their needs , most people use calculators , specialized software , and canned spreadsheet functions like Excel or , custom spreadsheet formulas , or calculators calculators . Its time once again to get a little practice . Don worry these are easy enough to work out on your own . EXERCISES Assume no default risks or transaction costs . What is the price of a 10 percent coupon bond , payable annually , with a 100 face value that matures in years if interest rates are percent ?

If interest rates were percent , how much would you give today for a loan with a balloon principal payment due in a year and that will pay in interest at the end of each quarter , including the final quarter when the principal falls due ?

What is the value today ofa share of stock that you think will be worth 50 in a year and that throws off in dividends each quarter until then , assuming the market interest rate is 10 percent ?

What is the value today ofa share of stock that you think will be worth 50 in a year and that throws off in dividends each quarter until then if the market interest rate is percent ?

KEY TAKEAWAYS Debt discount bonds , simple loans , fixed payment loans , and coupon contracts that promise payment in the future . They are priced by calculating the sum of the present value of the promised payments . URL books 74 What the Yield on That ?

LEARNING OBJECTIVE . What is yield to maturity and for what types of financial instruments is the yield to maturity relatively easy to calculate ?

Thus far , we have assumed or been given a market interest rate and then calculated the price ( of the instrument . Or , given the and an interest rate , we ve calculated the . Sometimes it is to do the opposite , to calculate the interest rate or , yield to maturity , the . Say that you know that someone paid 750 for a zero coupon bond with a face value of that will mature in exactly a year and you want to know what interest rate he or she paid . You know that ( i ) Solving for i Multiply each side of the equation by ( Multiply the terms on the side ofthe equation I Subtract from each side ofthe equation I Vi Divide each side of the equation by i ( I ) So in this case i ( 750 ) or percent . You can check your work by reversing the is , asking how much you pay today for in a year if interest was at percent ( 750 . Voila ! Stop and Think Box Suppose you have to invest for a year and two ways of investing it ( each equal in terms of risk and liquidity ) a discount bond due in one year with a face value of for 912 or a bank account at percent compounded annually . Which should you take ?

Choose the bond , which will yield percent ( 1000 912 ) 912 . To maximize your haul , invest the 88 left over from the purchase of the bond in the bank account . URL books 75 Calculating the yield to a perpetual debt , one with no maturity or repayment date , like a Consol , ground rent , mortgage , is also quite easy . The price or of a perpetuity is equal to the yearly payment divided by the going rate of interest ( So a ground rent that pays 50 a year ( a percent coupon rate ) would be worth if interest rates were percent , less if rates are higher , more if lower Calculating the yield to maturity of a perpetuity , if given the and , is easily done by taking the equation and solving for i Multiply each side by i Divided by i So the yield to maturity of a ground rent that pays 60 per year and that currently sells for 600 would be 10 percent i 10 . Stop and Think Box A ground rent contract consummated in Philadelphia , Pennsylvania , in 1756 is still being paid today . Someone recently paid 455 for the annual payment . What is the ground rent yield to maturity ?

If the interest rate rises to 10 percent , how much will the ground rent be worth ?

What if interest falls to percent ?

i so i . Calculating yield to maturity for coupon bonds and loans , however , is mathematically nasty business without a computer or bond table . In the past , people used to estimate the yield to maturity on such instruments by pretending they were or engaging in interpolation . In the first method , you use the easy perpetuity equation above ( i ) to get a URL books 76

quick estimate called the current yield . Unfortunately , current yield can be wide of the mark , especially for bonds with less than twenty years and bonds their par value . In the second method , one backs into the yield to maturity by making successive guesses about i and plugging them into the formula . Not fun , but you eventually get there . Most people today therefore use a calculator , spreadsheet , or utility rather than such erroneous ( current yield ) or laborious ( interpolation ) processes . You should be able to calculate the yield to maturity of discount bonds or by hand , or at worst with the aid of simple ( calculator . Here is a little practice . EXERCISES . A 100 bond payable in a year sells for . What is the yield to maturity ?

Sam promises to pay Joe in a year gives him today . What interest rate is Sam paying and what interest rate Joe is earning ?

Every year , the government pays a certain Indian tribe and , by terms of its treaty with that tribe , must do so forever . Trump offered to purchase the right to receive that stream for a payment of . What yield to maturity did Trump offer the Indians ?

What is the yield to maturity of a British Consol paying per year that sold for ?

KEY TAKEAWAYS Yield to maturity is the most economically accurate way of measuring nominal interest rates . It is easily calculated for discount bonds i ( and i where is the coupon or annual payment . Current yield is simply the yield to maturity of a perpetuity , so the more like a perpetuity a bond is , the better the current yield will approximate its yield to maturity . The shorter the maturity of a bond , the less like a Consol it is , so the less accurate the current yield formula will be . Similarly , the current yield works better the closer a bond price is to par because yield to maturity equals the coupon rate when the bond is at par . As the price deviates further from par , the less well the current yield can approximate the yield to maturity . URL books 77

Calculating Returns LEARNING OBJECTIVE . What is the rate of return and how does it differ from yield to maturity ?

This is not all you need to know about bonds ifyou were to become a bond trader because the bond market , which in the United States is over 200 years old , has some odd conventions that do not make much economic sense . Most students will not become professional bond traders , so in the interest of sanity , yours and ours , we will not delve into the intricacies here . If you do become a bond trader , you will quickly and easily pick up on the conventions anyway . Our goal here is to understand the basics of , yield to maturity ( and , finally , rate of return . Students sometimes the last two concepts . The yield to maturity is merely a measure of the interest rate . The rate of return is more a measure ofhow lucrative an investment is because it changes in the price ofthe bond ( or other asset , or otherwise ) More formally , where return from holding the asset for some time period , to to the price at time ( this can also be thought of as the purchase price ) Pu the price at time ( this can also be thought of as the sale or going market price ) coupon ( or other ) payment So imagine you purchased a percent coupon bond with a 100 face value that matures in three years when the interest rate is percent . As we learned above , the market price of such a bond would equal its face value , or 100 . We also learned that and interest rates are inversely related . As the market interest rate increases , the of the bonds future payments decreases and the bond becomes less valuable . As the rate decreases , the of future payments increases and the bond becomes more valuable . If the interest rate increased ( decreased ) to ( percent , the value of the bond would decrease ( increase ) so the returns you earned on the bond would not equal the yield to URL books 78

maturity . For example , suppose you purchased the bond for 100 but its price a year hence stood at 103 because interest rates decreased a little . Your return would be ( 100 , or . But if in the next year , interest rates soared , driving the market price of the bond down to 65 , your return ( from purchase ) would be ( 10 35 ) 100 or negative 25 . Yes , negative . It is quite possible to lose wealth by investing in bonds or instruments , even ifthere is no default ( even if payments are punctually made as promised ) Stop and Think Box As part of its effort to repay the large debts it accrued during the Revolutionary War , the federal government in the early issued three types of bonds a coupon bond that paid percent per year , a coupon bond that paid percent per year , and a zero coupon bond that became a percent coupon bond in 1801 . For most of the and early , the price of the percent bonds hovered around par . Given that information , what was the yield to maturity on government debt in that period ?

What , in general terms , were the prices of the percent and zero coupon bonds ?

The yield to maturity was about percent because the percent coupon bonds traded at around par . The price of the percent coupon bonds must have been well below par because who would pay 100 to get a year when she could pay 100 and get a year ?

Finally , the zeroes must have appreciated toward the price of the percent coupon bonds as the conversion date neared . Note that the loss is not , repeat not , predicated on actually selling the bond . One way to think about this is that the rate of return formula merely calculates the return if the bond were to be sold . Another way to think about it is to realize that whether the bond is sold or not , its owner is still poorer by the amount of the loss because the value of his assets , and hence his net worth , has shrunk by that amount . The risk of such loss is known as interest rate risk to distinguish it from other types of risks , like default risk ( the risk of nonpayment ) Interest rate risk is higher the longer the maturity of a bond because more are affected by increasing the interest rate , and the most distant ones are the most highly affected . Check this out The of in 10 years at compounded annually is ( At 10 it is , a loss of . The of in 30 years at and 10 is ( and ( so , respectively , a loss of URL books 79

percent . Duration is a technical measure of interest rate risk that we will not investigate here , where the main point is merely that rising interest rates hurt bond prices ( and hence ) falling interest rates help bond prices . KEY TAKEAWAYS The rate of return accounts for changes in the market price of a bond or other asset while the yield to maturity does not . Yield to maturity ( is almost always positive but returns are often negative due to interest rate risk , the risk that interest rates will rise , depressing bond prices . When the market interest rate increases , bond prices decrease because the opportunity cost of lending money has increased , making bonds less attractive investments unless their price falls . Algebraically , i ) The interest rate is in the denominator , so as bigger , must get smaller . Bonds with longer periods to maturity have more volatile prices , because the of their distant shrinks more , to very small sums . URL books 80

Inflation and Interest Rates LEARNING OBJECTIVE . What is the difference between real and nominal interest rates and why is the distinction important ?

You might well ask at this point , What factors change interest rates ?

One big factor is . As the price level rises , so too do interest rates , or at least what economists call nominal interest rates , the type of rates we ve discussed so far . If nominal rates do not increase ( and they often don , or can ) lenders might receive more nominal dollars than they lent but actually get back less purchasing power . Imagine , for example , that you lent 100 for one year at percent interest when a loaf of bread , pack of chewing gum , and bottle of Mountain Dew each cost . At the end of the simple loan , you would get back 100 106 and be able to enjoy an extra of goods , say , two loaves of bread , two packs of gum , and two bottles of the caffeine and sugar rush known as Doin the Dew . But what if prices doubled over that year ?

Instead of some combination of 106 goodies , you be able to buy only . Your nominal return would be positive , but your real return , what you could actually buy with the 106 , would be steeply negative . A simple equation , the Fisher Equation , named after Irving Fisher , the early economist who articulated it , helps us to understand the relationship between and interest rates more precisely i ir or , rearranging the terms , i or , again rearranging the terms , where i , the real interest rate i the nominal interest rate ( the type of interest rate the first part of this chapter discussed exclusively ) or expected ) Figure US . real interest rate , URL books 81

Percent ?

35 Date In plain English , after the fact ( ex post in economists lingo ) the nominal interest rate is equal to the real interest rate plus actual . Before the fact ( ex ante in economists lingo ) the nominal interest rate is equal to the real interest rate plus the expectation of . Stop and Think Box In early 2007 , a man had a wallet returned that he had lost over sixty years earlier in France , during World War II . In addition to his original Social Security card and a picture of his parents , the man received an sum of cash . Was losing the wallet a good investment ?

Why or why not ?

No , because the risk that it would never be returned was very high . Plus , the dollar lost a amount of its purchasing power over the period due to and the money earned no interest . At just percent compounded annually , 100 would have grown to 100 ( after 60 years . At percent , 100 would have grown to 100 ( URL books , 82

Traditionally , expectations were unobservable so real rates were known only ex post . However , relatively new and special types of bonds indexed to , called Treasury Protection Securities ( TIPS ) provide real interest rate information , allowing market participants to observe ex ante expectations . For example , if the yield to maturity on a regular , Treasury bond is percent , and the yield on the TIPS is percent , the expectation , via the Fisher Equation if , is percent . Figure US . real interest rate , shows how expectations have waxed and waned since the introduction of TIPS in 1997 . KEY TAKEAWAYS The difference between the real and the nominal interest rate is literally inflation or inflation expectations . According to the Fisher Equation , nominal interest equals real interest plus inflation ( or inflation expectations ) or real interest equals nominal interest minus inflation ( expectations ) If actual inflation exceeds inflation expectations , real ex post ( after the fact ) returns on bonds can be negative . To be frank , Benjamin Franklin and other colonists in America understood it well . ABC News video , Wallet Returned , 60 Years Later , A World War II Veteran gets his wallet returned to him sixty years ( URL books 83

Suggested Reading Fisher , Irving . The Purchasing Power ofMoney Its Determination and Relation to Credit Interest and Crises . New York Classics , 2006 . Gary . Investing in Fixed Income Securities Understanding the Bond Market . John Wiley and Sons , 2005 . Wild , Russell Bond Investing for Dummies . John Wiley and Sons , 2007 . URL books I 84