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Chapter 4 Interest Rates and Present Value

Chapter 4 Interest Rates and Present Value. Chapter Outline. Interest Rates Present Value. Interest Rates. The Market for Money. Interest Rate.

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Chapter 4 Interest Rates and Present Value

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  1. Chapter 4 Interest Rates and Present Value

  2. Chapter Outline • Interest Rates • Present Value

  3. Interest Rates The Market for Money

  4. Interest Rate • The 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.

  5. Interest rate (r) Supply r* Demand Money ($) Borrowed/Saved $* Figure 1 The Market for Money

  6. Nominal vs. Real Interest Rates • Nominal Interest Rate: the advertised rate of interest • Real Interest Rate: the rate of interest after inflation expectations are accounted for; the compensation for waiting on consumption

  7. Present Value • Present 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 rate n is the number of years until the payment is received/made.

  8. The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations)

  9. Examples From This Table • If 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.

  10. Mortgages, Car Payments, and other Multiple-Payment Examples • Mortgages 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.

  11. A Multiple Year Example Suppose 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.

  12. Monthly Payments Required on per $1000 of loan(For Several Interest Rates and Loan Durations)

  13. Examples From This Table • If 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.

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