1.1 Interest provides lenders with an incentive to supply credit. Interest also compensates lenders for inflation, default risk, and the opportunity cost of not being able to spend their money while it is lent out.

1.2 After two years, you would have: $1,000 ´ (1 + 1.03)2 = $1,060.90

1.3 Present value (PV) = $1,200/(1 + 0.10) = $1,090.91

1.6 a. CD 1: $1,000 x (1 + 0.05)3 = $1,157.63
CD 2: $1,000 x (1 + 0.08) x (1 + 0.05) x (1 + 0.03) = $1,168.02
You should choose CD 2 because it gives you the largest amount (or highest future value) after three years.

b. CD 2: $1,000 ´ (1 + 0.01) ´ (1 + 0.01) ´ (1 + 0.10) = $1,122.11. CD 1 has the higher future value, so you should now choose CD 1 rather than CD 2.

c. CD 3: $1,000 ´ (1 + 1.03) ´ (1 + 1.03) ´ (1 + 1.07) = $1,135.16. CD 3 has a lower future value than the other two.

2.1 Debt instruments include loans granted by banks or bonds issued by corporations and governments. Equities represent part ownership of the firm that issues them.

2.2 The four basic categories of debt instruments are simple loans, discount bonds, coupon bonds, and fixed-payment loans. Coupon bonds and fixed-payment loans pay interest before the instrument matures. Fixed-payment loans pay back principal before the instrument matures.

2.3 a. Fixed-payment loan

b. Coupon bond

c. Discount bond

d. Fixed-payment loan

3.1 The yield to maturity is the interest rate that equates the present value of future payments of a debt instrument with its current price. The yield to maturity is a better measure of the interest rate than the coupon rate because the coupon rate does not take into account that the purchase price of a bond may differ from the face value of the bond. An investor buying a bond with a price greater than its par value will be earning an interest rate, as measured by the yield to maturity, that is lower than the coupon rate on the bond. An investor buying a bond with a price lower than its par value will be earning an interest rate, as measured by the yield to maturity, that is greater than the coupon rate on the bond.

3.2 a.

b. i = (Required loan payment - principal)/principal

c. i =

d. Loan value =

3.3 At the 10% interest rate:

The present value of $75 one year from now is: $75/(1 + 0.10) = $68.18.

The present value of $85 two years from now is: $85/(1 + 0.10)2 = $70.25.

The present value of $90 three years from now is: $90/(1 + 0.10)3 = $67.62.

Because the present value is highest if you receive $85 in two years, you would prefer to receive that payment.

The 20% interest rate compared to the 10% interest rate increase the present value of funds received sooner. At the 20% interest rate:

The present value of $75 one year from now is: $75/(1 + 0.20) = $62.50.

The present value of $85 two years from now is: $85/(1 + 0.20)2 = $59.03.

The present value of $90 three years from now is: $85/(1 + 0.20)3 = $52.08.

With an interest rate of 20%, you would prefer to receive a payment of $75 in one year because it has the highest present value.

3.4 The present value of two one-year subscriptions is $60 + $60/(1 + 0.10) = $114.55. The present value of a two-year subscription is the $115 you pay for the subscription. So, you can save a small amount in present value terms if you take out two one-year subscriptions rather than a two-year subscription.

3.5 We now the following must be true for this bond: $870 = $1,000/(1 + i)2. So, we need to solve for the yield to maturity, i.

$870(1 + i)2 = $1,000

(1 + i)2 = $1,000/$870

i = (($1,000/$870)1/2 – 1) × 11 = 7.21%

3.6 a. $350,000 = $475,000/(1+i)5

b. $720 = $1,000/(1+i)5

c. $950 = $80/(1+i) + $80/(1+i)2 + $80/(1+i)3 + $80/(1+i)4 + $80/(1+i)5 + $80/(1+i)6 + $1,000/(1+i)6

d. $4,000 = $275/(1+i)3 +$275/(1+i)4 +… + $275/(1+i)22

3.7 $450 = $62.5/(1+i)11 + $62.5/(1+i)12 + $62.5/(1+i)13 + ….+ $62.5/(1+i)30 + $1000/(1+i)30

3.8 In effect, the payments to Ed were like those of a perpetuity or consol. Therefore, the relevant interest rate would be ($135/$1,125) × 35/ = 12%.

3.9 a. $100,000 = $10,000/(1 + i) + $10,000/(1 + i)2 + … + $10,000/(1 + i)20

b. Thinking in terms of the arithmetic, if David dies after 40 years instead of 20 years, we have to add another 20 terms to the right side of the equation in part (a). The only way for the value of those 40 terms to still equal $100,000 is if the interest rate is higher than in part (a). Thinking in terms of the economics, David is now receiving 40 annual $10,000 payments for his $100,000 investment, so the interest rate must be higher.

4.2 A capital gain is an increase in the price of an asset. If market interest rates increase, bond prices fall, so you will experience a capital loss.

4.7 a. A coupon rate of 5% means that the bond pays a $50 annual coupon. A bond’s current yield equals its coupon divided by its current price = ($50/$955.11) × 100 = 5.24%

b. The bond’s price is lower than its face value, which raises the yield to maturity above the coupon rate. The yield to maturity on the bond reflects the current market interest rate, while the coupon rate reflects the (lower) market interest rate at the time the bond was first issued.

5.1 Yield to maturity is the return on a bond assuming the bondholder holds the bond for the full maturity. Rate of return is the return over a specific holding period that takes into account the coupon received during the period and any change in the price of the bond during the period.

5.2 Interest-rate risk is the risk that changes in market interest rate will cause changes in the price of a bond. A given change in interest rates has a larger effect on the present value, and therefore the price, of a long-term bond than a short-term bond. Table 3.2 on page 75 of the text provides an example of the effect of maturity on interest-rate risk.

5.3 To calculate the rate of return (R), we need to add the coupon received to the capital gain and divide by the purchase price of the bond. With a 4% coupon rate, you received a $40 coupon. You also earned a capital gain of: $1,150 - $950 = $200. So, your rate of return during this one-year holding period was: R = (($40 + $200)/$950) ´ 100 = 25.26%.

6.1 Nominal interest rates are not adjusted for inflation. Real interest rates are adjusted for inflation.

6.3 TIPS, which stands for Treasury Inflation Protection Securities, are indexed bonds, which means that the Treasury increases the bonds’ principal as the price level rises. Because the principal increases with inflation, so does the interest rate on the bond. An investor would buy TIPS rather than conventional Treasury bonds to protect against increases in inflation.

6.5 The difference between the real interest rate and the expected real interest rate exists because the future inflation rate is unknown, causing the actual inflation rate to often differ from the expected inflation rate. This possible difference would be more of a concern for a 10-year loan than for a 1-year loan because the actual inflation rate could differ more from the expected inflation rate for a 10-year period than a 1-year period. In particular, if the inflation rate were to be persistently higher over the 10-year period than you had expected when you made the loan, you would be receiving a lower than expected real interest rate during the 10 years.