Chapter 4: Interest Rates and Present Value

Chapter 4 Interest Rates and Present ValueChapter OutlineInterest RatesPresent ValueInterest RatesThe Market for MoneyInterest RateThe interest rate is the percentage, usually expressed in annual terms, of a balance that is paid by a borrower to a lender that is in addition to the original amount borrowed or lent.Figure 1 The Market for MoneySupplyDemandr*$*Interest rate (r) Money ($) Borrowed/SavedNominal vs. Real Interest RatesNominal Interest Rate: the advertised rate of interestReal Interest Rate: the rate of interest after inflation expectations are accounted for; the compensation for waiting on consumptionPresent ValuePresent Value is the interest adjusted value of future payment streams.Mathematically, the present value of a payment is =(payment)/(1+r)n Where r is the interest raten is the number of years until the payment is received/made.The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations)Interest rate -> Years 20%10%5%2%1%30237.3817.454.321.811.35106.192.591.631.221.1052.491.611.281.101.0511.201.101.051.021.01Examples From This TableIf you borrow $1 and promise to pay it back in 5 years at 5% interest you will owe $1.28 which is the original $1 plus 28 cents in interest. If you borrow $1 and promise to pay it back in 30 years at 20% interest you will owe $237.38 which is the original $1 plus $236.38 in interest.Mortgages, Car Payments, and other Multiple-Payment ExamplesMortgages are loans taken out to buy homes. Typically you borrow a large sum of money and promise to pay it back in even amounts each month for 10, 15, or 30 years.Car loans are similar to mortgages in that you borrow a large sum but the loan duration is usually two to six years.A Multiple Year ExampleSuppose you pay $100 for the first 5 years then receive $100 for the next 7 years. The present value of the can be depicted in the picture below. For instance the present value of the $100 paid in the fifth year is $100/(1.10)4 or $68.30.Monthly Payments Required on per $1000 of loan(For Several Interest Rates and Loan Durations)Interest rate -> Years 20%10%5%2%1%3016.718.785.373.703.221019.3313.2210.619.208.76526.4921.2518.8717.5317.09192.6387.9285.6184.2483.79Examples From This TableIf you borrow $1000 and promise to pay it back monthly over 5 years at 5% interest you will owe $18.87 per month.If you borrow $1000 and promise to pay it back monthly over 10 years at 20% interest you will owe $19.33 per month.