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Chapter 4 Interest Rates and Present

Value

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Chapter Outline

• Interest Rates• Present Value

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Interest Rates

The Market for Money

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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.

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Figure 1 The Market for Money

Supply

Demand

r*

$*

Interest rate (r)

Money ($) Borrowed/Saved

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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

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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 raten is the number of years until the payment is

received/made.

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The Amount Payable for Every Dollar Borrowed

(For several interest rates and loan durations)

Interest rate -> Years

20% 10% 5% 2% 1%

30 237.38 17.45 4.32 1.81 1.35

10 6.19 2.59 1.63 1.22 1.10

5 2.49 1.61 1.28 1.10 1.05

1 1.20 1.10 1.05 1.02 1.01

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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.

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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.

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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.

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Monthly Payments Required on per $1000 of loan

(For Several Interest Rates and Loan Durations)

Interest rate -> Years

20% 10% 5% 2% 1%

30 16.71 8.78 5.37 3.70 3.22

10 19.33 13.22 10.61 9.20 8.76

5 26.49 21.25 18.87 17.53 17.09

1 92.63 87.92 85.61 84.24 83.79

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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.