INTEREST RATE DETERMINATIONPowerPoint PresentationTHE MARKET FOR LOANABLE FUNDSNote that the demand curve for loanable funds is negatively sloped (like every other demand curve). Why would a reduction in the interest rate increase the quantity demanded of loanable funds?BASICS OF COMPOUND INTERESTTHE FORMULA FOR FUTURE VALUENOW WE SET A DIFFERENT QUESTIONSlide 8Slide 9Slide 10Slide 11Present Value DefinedP(0) = P(t) / (1 + i)tSlide 14WHAT’S THE PV OF $10,000 t YEARS HENCE?Slide 16Slide 18EXAMPLESlide 22Slide 24Slide 25NET PRESENT VALUEEXAMPLE:Slide 29Slide 31Slide 32ANOTHER VIEW:Slide 34INTERNAL RATE OF RETURNSlide 36Slide 37AN APPLICATION TO EDUCATIONSlide 39Slide 40Incomes over your life if you have a high school education.If you go to college you might get a higher income.Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Interest rates slide 1INTEREST RATE DETERMINATIONINTEREST RATE DETERMINATIONThe rate of interest is the price of money to borrow and lend. Rates of interest are expressed as decimals or as percentages. For example, the rate of interest of 5 percent per year(5%) could be written as i=.05.Interest rates slide 2One theory views the rate of interest as the price in the market for loanable funds.Loanable funds are monies borrowed by firms from consumers in order to undertake investment projects.[NOTE: Investment = additions to capital stock, such as factories, houses, inventories, etc. Investment is not buying stocks and bonds.]Interest rates slide 3THE MARKET FOR LOANABLE FUNDSinterestratesupply of loanable fundsdemand for loanable fundsQLOANABLE FUNDSQEiEInterest rates slide 4Note that the demand curve for loanable funds is negatively sloped (like every other demand curve).Why would a reduction in the interest rate increase the quantity demanded of loanable funds?This is a question with a complicated answer.We begin with the idea of compound interest.Interest rates slide 5BASICS OF COMPOUND INTERESTBASICS OF COMPOUND INTERESTSuppose I put on deposit today $1,000 at a rate of interest of 5 percent (i = .05).After one year my balance becomes$1,000 + .05($1,000) = (1 + .05)$1,000If interest is compounded annually, after two years my balance will be(1 + .05)((1 + .05)$1,000)) = (1 + .05)2$1,000.Interest rates slide 6THE FORMULA FOR FUTURE VALUETHE FORMULA FOR FUTURE VALUEIn general, a current balance of P(0) placed on deposit for t years at a rate of interest i (compounded annually) becomes P(t) = P(0) (1 + i)t.P(t) is called the future value of the current balance.Interest rates slide 7NOW WE SET A DIFFERENT QUESTIONSuppose I want to have a fixed amount of money available to me in the future.How much money would I have to put aside today to get the future amount? Remember that what I put aside today accumulates at a compound annual rate of interest, i.Interest rates slide 8For example, suppose I want to have $25,000 available 5 years from now to buy a new car.How much would I have to put on deposit today, if the rate of interest is 6 percent, so that I will have the $25,000 when I need it?Interest rates slide 9The answer to the question can be found in the basic formula for compound interest:P(t) = P(0) (1 + i)tWe know P(t), the amount we want in the future, and we know i and t.We need to find P(0), the amount to put on deposit today that will become P(t), t years in the future if the rate of interest is i.Interest rates slide 10In the example, P(t) = $25,000, t = 5, and i = .06.So we have$25,000 = P(0) (1 + .06)5Therefore, P(0) = $18,681.45.Interest rates slide 11P(0) is the called the present value of $25,000., 5 years hence, at 6 percent.Interest rates slide 12Present Value DefinedThe Present Value of a future amount is the amount of money I would have to put on deposit today so that today’s deposit would eventually become the future amount at the going compound rate of interest.Here’s another way to say it:The Present Value of P(t) dollars t years in the future is the amount that must be put on deposit today at a rate of interest, i, so that the deposit equals P(t) after t years.Interest rates slide 13P(0) = P(t) / (1 + i)tNote that the present value of P(t) dollars falls with increases in the rate of interest, i.This is just another way of saying that if the rate of interest is higher, you don’t have to put away as much today to reach your goal.Interest rates slide 14Note also that the present value of P(t) falls with increases in t.This is just another way of saying that the farther in the future you want the money, the less you have to put aside today.slide 15Interest ratesWHAT’S THE PV OF $10,000 t YEARS HENCE?t 5% 10%0 10000 100001 9524 90912 9070 82643 8638 75134 8227 68305 7835 62096 7462 56457 7107 51328 6768 46659 6446 424110 6139 385511 5847 350512 5568 3186Interest rates slide 16Example: Your friend will give you $200 two years from today. What is the present value of the gift?Interest rates slide 18Example: Your aunt Alice offers you the choice between two gifts. The first is a cash gift today of $5,000 to cover your college costs. The second is a cash gift 5 years from now of $8,000 to help you buy a new car. Which gift do you choose? [Hint: Choose the one with the greater present value.]Interest rates slide 20EXAMPLEA rich alumnus decides to leave funds for an endowed chair to the university. The gift will be made when he dies, which is predicted to be in 20 years. His gift at that time will be $5 million.In order to assure that the funds will be paid the alum sets up a trust. If the interest rate is 7%, what is the PRESENT VALUE of $5 million 20 years hence? That is to say, how much money must he deposit in the trust today?Interest rates slide 22EXAMPLEYou buy a bond that promises to pay you $100 (in interest) in each of the next 3 years ($100 one year from now, $100 two years from now, etc.)At the time you get the third interest payment you receive the principal on the bond of $1,000.How much do you pay for the bond?Interest rates slide 24The concept of PRESENT VALUE allows us to compare the values of returns and costs that may accrue at different times in the future.For example, which would you prefer, $1,000 now or $1,200 one year from now? If you are like most people you will choose the one that has the greatest present value. And which asset has the greater PV depends on the rate of interest.Interest rates slide 25The PV of $1,000 today is $1,000 (= 1,000/(1+i)0)The PV of $1,200 one year