Interest Rates

Chapter 5.1-5.3

Outline

• Interest Rate Quotes and Adjustments– The Effective Annual Rate (EAR) and the Annual

Percentage Rate (APR)• The determinants of Interest Rates– Real versus Nominal Interest Rates– The Yield Curve

• Further questions

Interest Rates Quotes and Adjustments

The Effective Annual Rate (EAR)

• The effective annual rate reflects the dollar interest received from investing $1 for 1 year. This is the rate we have been considering up till now.

• This EAR is often quoted as “Annual Percentage Rate” or “APR” when payments are made throughout the year such as mortgages, car loans and other investments

Effective Annual RateInterest rates for periods smaller than one year:• Given a certain EAR we can calculate the interest accumulated

for a shorter period than one year.

Example: Receiving 5% for one year is equivalent to receiving 2.47% every six months

At the end of the first six months we have $1.0247. If this amount is reinvested for the rest of the year, then $1.05 is accumulated in total

Effective Annual Rate

Annual Percentage Rate (APR)

The annual percentage rate (APR) indicates the amount of simple interest earned in one year, that is the amount without the effect of compounding – it does not fully take into account the time value of money

• The APR is quoted for a given number of compounding periods

• The compounding period can be “annual”, “semiannual”, “quarterly”, “monthly”, or even “daily”

Converting APR to EAR

The interest received per compounding period for an APR with k compounding periods is:

Converting APR to EAR

Converting APR to EAR

Annual Percentage Rate (APR)

Annual Percentage Rate (APR)

Application: Amortizing Loans

In amortizing loans each periodic payment is the same which means that each period you pay interest on the loan and some part of the loan balance.

Application: Amortizing

Loans

The Determinants of Interest Rates

Nominal and Real Interest Rates

Nominal interest rate: is the rate we have been using till now for discounting future cash flows and it indicates the rate at which your money will grow if invested for a certain period

Real interest rate: is the rate of growth of your purchasing power, after adjusting for inflation.

rR is the real interest rate

i is the rate of inflation

Interest Rates and Inflation

The Yield Curve of Interest Rates

Interest rates change depending on the horizon of the investment:• Banks often offer different rates on loans

depending on their term

The Yield Curve: depicts the Term Structure of interest rates or the relation between the investment term and the interest rate

The Term Structure of Risk-Free U.S. Interest Rates

Present Value Calculation

We can calculate the present value of a stream of cash flows using the term structure of interest rates

Present Value Calculation

Further questions

CollegeQuestion 10 (2nd Edition): Your son has been accepted into college. This college guarantees that your son’s tuition will not increase for the four years he attends college. The first $10,000 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (semiannual) guaranteed to remain the same over the next four years.

How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made?

CollegeEight payments of $10,000 due semiannually and starting six months from now. The six month interest rate is

The required deposit to cover all future tuition expenses

Car Dealer LoanQuestion 22 (2nd Edition): You need a new car and the dealer has offered you a price of $20,000, with the following payment options: (a) pay cash and receive a $2000 rebate, of (b) pay a $5000 down payment and finance the rest with a 0% APR loan over 30 months. But having just quit your job and started an MBA program, you are in debt and you expect to be in debt for at least the next 2.5 years. You plan to use credit cards to pay your expenses; luckily you have one with a low (fixed) rate of 15% APR (monthly).

Which payment option is best for you?

Car Dealer LoanThe car dealer is offering tow alternatives:

(a) A loan at 0% APR compounded monthly – or in other words: an initial payment of $5,000 and 30 monthly payments of $500 thereafter.

(b) $2,000 rebate.

The cost of the car under dealer financing is: