Money And Banking [ch. 4]

The yield to maturity is the most accurate measure of interest rates because it takes into account the current market price of a bond, the coupon rate, and the time remaining until maturity. It represents the total return an investor can expect to receive if they hold the bond until it matures, including both the coupon payments and any capital gains or losses. This measure considers the time value of money and provides a comprehensive assessment of the bond's profitability.

The explanation for the given correct answer is that yield to maturity is a term used in finance to represent the total return anticipated on a bond or other fixed-interest security if it is held until it matures. It includes both the interest earned and any capital gain or loss. Economists often refer to yield to maturity as the "interest rate" because it represents the overall return on the investment. Therefore, the statement is true.

The statement is true. The coupon rate on a bond is calculated by dividing the coupon payment by the face value (also known as the par value) of the bond. The coupon payment is the fixed interest payment that the bondholder receives annually or semi-annually. The coupon rate is expressed as a percentage and represents the yield that the bondholder will receive based on the bond's face value.

The coupon rate of a bond is the annual interest payment divided by the face value of the bond. In this case, the bond has a face value of $1,000 and pays an annual coupon of $100. Therefore, the coupon rate is $100 divided by $1,000, which is equal to 0.1 or 10%.

The real interest rate is not 9% when the nominal interest rate is 7% and expected inflation is 2%. The real interest rate is calculated by subtracting the expected inflation rate from the nominal interest rate. In this case, the real interest rate would be 5% (7% - 2%). Therefore, the correct answer is false.

When the nominal interest rate is high (15%) and the expected inflation rate is also high (13%), borrowers have a greater desire to borrow. This is because the real interest rate (the nominal interest rate minus the inflation rate) is lower in this scenario. Borrowers are more likely to take loans when they can borrow at a lower real interest rate, as it makes borrowing more affordable. On the other hand, when the nominal interest rate is low (6%) and the expected inflation rate is also low (2%), the real interest rate is higher, making borrowing less attractive. Therefore, the statement "Borrowers have a greater desire to borrow when the nominal interest rate is 15% and the expected inflation rate is 13% than when the nominal interest rate is 6% and the expected inflation rate is 2%" is true.

A fixed-payment loan does not require the borrower to make a single payment when the loan matures. Instead, it requires the borrower to make equal monthly payments over the life of the loan, which includes both the principal and interest.

The simple interest on this loan can be calculated by subtracting the principal amount from the total amount to be repaid and then dividing it by the principal amount. In this case, the total amount to be repaid is $106.50 and the principal amount is $100. So, the interest is $6.50. To find the interest rate, we divide the interest by the principal amount and multiply by 100. Therefore, the interest rate is 6.5%.

The statement is true because the price of a bond and its yield to maturity have an inverse relationship. When the yield to maturity increases, the price of the bond decreases, and vice versa. This is because as the yield to maturity increases, the bond becomes less attractive to investors, causing its price to decrease in order to compensate for the higher yield. Conversely, when the yield to maturity decreases, the bond becomes more attractive, leading to an increase in its price.

The real interest rate is calculated by subtracting the expected rate of inflation from the nominal interest rate. In this case, the nominal interest rate is 4% and the expected rate of inflation is 2%. Subtracting 2% from 4% gives us a real interest rate of 2%.

The price of a bond is determined by the present value of its future cash flows, which include both the coupon payments and the final principal payment at maturity. In this case, the bond pays annual coupons of $50 for two years, so the total coupon payments will be $50 x 2 = $100. The yield to maturity of 7% indicates the required rate of return for investors. By discounting the future cash flows at this rate, we can calculate the present value of the bond. The present value of the coupons can be calculated using the formula for the present value of an annuity, and the present value of the principal payment can be calculated using the formula for the present value of a single payment. Adding these present values together will give us the price of the bond, which in this case is $963.84. Therefore, the statement is true.

When market participants expect inflation in the future, nominal interest rates will exceed real interest rates. This is because nominal interest rates include the expected inflation rate, while real interest rates adjust for inflation by subtracting the expected inflation rate. Therefore, if there is an expectation of inflation, the nominal interest rate will be higher than the real interest rate.

A coupon bond is a type of instrument that pays the holder a fixed interest payment every year until maturity. At maturity, the holder is also paid the face value or principle of the bond. This means that the holder receives both regular interest payments and the full amount of their initial investment at the end of the bond's term. This distinguishes a coupon bond from other options listed, such as simple loans or fixed-payment loans, which may not have regular interest payments or a fixed maturity date. A discount bond, on the other hand, is sold at a discount to its face value and does not pay regular interest payments.

If the yield to maturity on a bond exceeds its coupon rate, it means that the bond is selling at a discount. When a bond is selling at a discount, its price is below its face value, not above it. Therefore, the given statement is incorrect, and the correct answer is False.

The statement is false because the security that pays the holder $500 five years from today is not preferred to a security that pays the holder $100 per year for the next five years. The second security provides a consistent annual payment over the five-year period, whereas the first security only provides a single payment after five years. The consistent annual payments provide a more reliable and predictable income stream, making it a more preferred option for many investors.

The present value of the insurance settlement can be calculated using the formula for present value of an annuity. In this case, the annuity is $5,000 per year for three years, and the interest rate is 6%. Using the formula, the present value is calculated as $5,000 / (1 + 0.06)^1 + $5,000 / (1 + 0.06)^2 + $5,000 / (1 + 0.06)^3 = $4,716.98 + $4,452.99 + $4,996.99 = $14,166.96. Therefore, the correct answer is $14,166.96.

If the yield to maturity on a bond exceeds the coupon rate, it means that the bond is offering a higher return to investors than what they would receive from the coupon payments alone. This makes the bond less attractive in the market, causing its price to decrease. As a result, the price of the bond is below its face value.

The rate of return for the bondholder is calculated by taking into account the initial investment, the annual coupon payments, and the final sale price. In this case, the bondholder initially invests $1,000 and receives $40 in coupon payments for one year. After holding the bond for one year, the bondholder sells it for $1,050. To calculate the rate of return, we can use the formula: (Coupon payment + (Sale price - Purchase price)) / Purchase price. Plugging in the values, we get (40 + (1,050 - 1,000)) / 1,000 = 90 / 1,000 = 0.09 = 9%. Therefore, the rate of return for that year for the bondholder is 9%.

A U.S. Treasury bill is classified as a discount bond because it is sold at a discount to its face value and does not pay periodic interest payments. Instead, the investor receives the full face value of the bond at maturity. This means that the investor earns a return by buying the bond at a lower price and receiving the full face value when it matures.

The statement is true because a perpetuity is a type of investment that pays a fixed amount of income indefinitely. The current yield is calculated by dividing the annual interest payment by the current market price of the investment. Since the perpetuity has a fixed income and no maturity date, the current yield is equal to the yield to maturity, which represents the total return on the investment over its entire lifespan. Therefore, the current yield and yield to maturity on a perpetuity are the same.

The approximate yield to maturity on a discount bond can be calculated by using the formula: YTM = (Face Value - Purchase Price) / Purchase Price * (1 / Time to Maturity). In this case, the face value is $10,000, the purchase price is $9,174.31, and the time to maturity is 1 year. Plugging in these values, we get YTM = (10,000 - 9,174.31) / 9,174.31 * (1 / 1) = 0.09 or 9%. Therefore, the approximate yield to maturity on this bond is 9%.

If the interest rate falls by the same amount for both short-term and long-term bonds, bondholders would actually prefer to be holding long-term bonds. This is because when interest rates decrease, the value of existing bonds increases. Long-term bonds have a longer duration, meaning they have a higher sensitivity to interest rate changes. Therefore, when interest rates fall, the value of long-term bonds increases more than short-term bonds, making them more desirable for bondholders.

The coupon rate refers to the annual interest payment made by the issuer of a bond, expressed as a percentage of the bond's face value. It is calculated by dividing the coupon payment by the face value of the bond. The coupon rate is an important metric for bond investors as it helps determine the fixed income they will receive from the bond.

The statement is false because the present discounted value of a future cash flow is actually lower than the future cash flow. This is because money received in the present is worth more than the same amount of money received in the future due to the time value of money. Therefore, most people would prefer to receive $100 today rather than receiving the same amount in a year's time.

The bond with the highest yield to maturity is the one that is selling at the lowest price. In this case, the bond selling for $900 has the highest yield to maturity because it is being sold at a discount compared to its face value of $1,000. The discount increases the overall yield of the bond, making it the highest among the options given.

The approximate yield to maturity is calculated by finding the discount rate that equates the present value of the bond's future cash flows (coupon payments and the par value) to its current price. In this case, the bond has a par value of $1,000 and pays an annual coupon of $70. The price of the bond today is $1,019.05. By using the formula for yield to maturity, we can calculate that the approximate yield to maturity is 5%.

The yield to maturity on a U.S. Treasury bill is calculated by considering the purchase price, face value, and time to maturity. In this case, the bill is selling for $9,500, has a face value of $10,000, and matures in one year. To calculate the yield to maturity, we need to determine the discount rate that equates the present value of the bill's cash flows to its current price. However, the given information does not provide any interest rate or discount rate. Therefore, we cannot determine the yield to maturity based on the given information. Hence, the statement "The yield to maturity on a U.S. Treasury bill that sells for $9,500 today, has a face value of $10,000, and matures in one year, is 5%" is false.

The present value of a future amount of money is calculated by discounting it back to the present using an appropriate interest rate. In this case, the interest rate is given as 5%. To calculate the present value of $1,000 to be received five years from today, we use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. Plugging in the values, we get PV = $1,000 / (1 + 0.05)^5 = $783.53. Therefore, the correct answer is $783.53.

If the interest rate falls by the same amount on all bonds, the bond with the longest maturity would be preferred. This is because longer-term bonds are more sensitive to changes in interest rates, meaning their prices will increase more when interest rates fall. Therefore, holding a $10,000 U.S. Treasury bond with 20 years to maturity would be the preferred choice.

Current yield is a measure of the annual income generated by a bond, calculated by dividing the bond's annual interest payment by its market price. It does not take into account the bond's time to maturity or any potential price changes. Therefore, it is not a reliable estimate of yield to maturity for any type of bond, whether short-term or long-term. The yield to maturity takes into consideration the bond's coupon payments, its purchase price, and the time remaining until maturity, providing a more accurate measure of the bond's overall return.

When interest rates rise, bond prices will fall. This is because when interest rates increase, new bonds are issued with higher coupon rates, making existing bonds with lower coupon rates less attractive to investors. As a result, the demand for existing bonds decreases, causing their prices to decrease. Therefore, bondholders are displeased when interest rates rise because it leads to a decrease in the value of their bonds.

The rate of return can be calculated by taking into account the initial investment, the final value, and any coupon payments received. In this case, the bond was purchased for $1,000 and sold for $920 after one year. Additionally, the bond has a 5% coupon rate, which means that the investor would have received $50 in coupon payments over the year. Therefore, the total return can be calculated as the sum of the coupon payments ($50) and the difference between the final value and the initial investment ($920 - $1,000 = -$80). The rate of return is then calculated as the total return divided by the initial investment, which gives us (-$80 + $50) / $1,000 = -3%.

The price of a coupon bond is determined by the present value of its future cash flows. In this case, the bond has a coupon rate of 8% and a par value of $1,000. The coupon payments over the two-year period can be calculated as 8% of $1,000, which is $80 per year. The yield to maturity is 12%, which represents the required rate of return for investors. Using these values, the present value of the coupon payments can be calculated using the formula for the present value of an annuity. The present value of the par value can also be calculated using the formula for the present value of a single amount. Adding these two present values together will give the price of the bond, which is $932.40.

All of the statements provided are true. The current yield is indeed a better approximation of yield to maturity for long-term bonds compared to short-term bonds. Bond prices do vary inversely with the interest rate for both coupon bonds and discount bonds. The longer the maturity of a bond, the greater the change in its price for the same change in interest rate. Additionally, the coupon rate on a coupon bond is fixed once the bond is issued.

When the interest rate increases, the price of a perpetuity decreases. In this case, as the interest rate changes to 10%, the price of the perpetuity will fall. The decrease in the interest rate causes the present value of the perpetuity's future cash flows to decrease, resulting in a lower price. In this scenario, the price will fall by $500, as the perpetuity pays coupons of $50 per year.