Question

your current cd matures in a few days. you would like to find an investment with a higher rate of return than the cd. stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. you have been looking at bond listings in the newspaper. a friend wants you to look at the following corporate bonds as a possible investment.

bond	cur. yld	vol	close	net chg
xyz 7$\frac{3}{4}$ - 15	8.4	17	100$\frac{1}{2}$	+$\frac{1}{4}$

if you buy three of the abc bonds with $10 commission for each, how much will it cost?
a. $3142.50
b. $1047.50
c. $3172.50
d. $1077.50

Explanation:

Step1: Understand Bond Price

The close price for ABC bond is $104\frac{3}{4}$, which is $104.75$ (since $\frac{3}{4}=0.75$). Each bond has a par value? Wait, no, the close price here is the price per bond (usually as a percentage of par, but here it's given as $104\frac{3}{4}$, so we can take it as the price per bond in dollars? Wait, actually, bond prices are often quoted as a percentage of par (usually $1000$), but maybe here it's a typo? Wait, no, looking at the table, the "Close" for ABC is $104\frac{3}{4}$, and "Vol" is 128. Wait, maybe the bond has a par value of $1000$, and the price is $104\frac{3}{4}\%$ of par? Wait, no, the question is about buying three ABC bonds. Wait, maybe the "Close" is the price per bond in dollars, but that would be too low. Wait, no, probably the bond is a $1000$ par value, and the price is $104\frac{3}{4}$ dollars? No, that doesn't make sense. Wait, no, bond prices are typically quoted as a percentage of par, where par is $1000$, so $104\frac{3}{4}$ means $104.75\%$ of $1000$, so the price per bond is $1000\times1.0475 = 1047.5$? Wait, no, wait, maybe the "Close" is the price per bond in dollars, but that would be $104.75$ per bond, but then buying three would be $3\times104.75 = 314.25$, plus commission. But the options are in the thousands. So I must have misinterpreted. Wait, maybe the bond has a par value of $1000$, and the price is $104\frac{3}{4}$ (i.e., $104.75$) per $100$ par? No, that also doesn't fit. Wait, let's re-examine the problem.

Wait, the "Close" for ABC is $104\frac{3}{4}$, which is $104.75$. Let's assume that each bond has a face value of $1000$, and the price is $104.75$ dollars? No, that can't be. Wait, no, maybe the "Close" is the price per bond in dollars, and the bond has a par value of $1000$, but the price is $104.75$? No, that would be a very low price. Wait, I think I made a mistake. Wait, the problem says "buy three of the ABC bonds". Let's check the options. The options are $3142.50$, $1047.50$, $3172.50$, $31077.50$. Wait, $1047.50$ is one of the options (option b), but we are buying three. Wait, maybe the bond is a $1000$ par value, and the price is $104\frac{3}{4}$ (i.e., $104.75$) dollars? No, that's not right. Wait, no, the "Close" is $104\frac{3}{4}$, which is $104.75$, and each bond is $1000$ par, so the price per bond is $104.75$? No, that would be $104.75$ for a $1000$ par bond, which is $10.475\%$ of par, which is too low. Wait, I think I messed up the bond price notation. Actually, bond prices are quoted as a percentage of par (usually $1000$), so $104\frac{3}{4}$ means $104.75\%$ of $1000$, so the price per bond is $1000\times1.0475 = 1047.5$ dollars. Ah, that makes sense. So each ABC bond costs $1047.5$ dollars. Then, buying three bonds: $3\times1047.5 = 3142.5$ dollars. Then, add the commission: $10$ per bond, so $3\times10 = 30$ dollars. Wait, no, the commission is $10$ for each bond? Wait, the problem says "with $10$ commission for each". So total cost is (price per bond * number of bonds) + (commission per bond * number of bonds). So price per bond: $104\frac{3}{4} = 104.75$? Wait, no, if the bond is $1000$ par, and the price is $104.75$ (as a percentage of par), then price per bond is $1000\times1.0475 = 1047.5$? Wait, no, $104.75\%$ of $1000$ is $1047.5$ dollars. So three bonds: $3\times1047.5 = 3142.5$ dollars. Then commission: $10$ per bond, so $3\times10 = 30$ dollars. Total cost: $3142.5 + 30 = 3172.5$? Wait, no, wait, maybe the "Close" is the price per bond in dollars, and the bond has a par value of $100$, so $104.75$ per $100$ par, so for a $1000$ par bond, it's $1047.5$? No, I'm confused. Wait, let's look at the options. Option c is $3172.50$. Let's recalculate.

Wait, the "Close" for ABC is $104\frac{3}{4}$, which is $104.75$. Let's assume that each bond is a $1000$ par value, and the price is $104.75$ dollars? No, that can't be. Wait, maybe the bond is a $100$ par value, so $104.75$ per $100$ par, so each bond (if par is $1000$) would be $10\times104.75 = 1047.5$? No, this is getting too convoluted. Wait, let's do the math with the numbers. Let's take the "Close" as $104\frac{3}{4} = 104.75$ dollars per bond (assuming par is $100$). Then, buying three bonds: $3\times104.75 = 314.25$? No, that's too low. Wait, the options are in the thousands, so maybe the bond is a $1000$ par value, and the price is $104\frac{3}{4}$ (i.e., $104.75$) dollars? No, that's impossible. Wait, I think the mistake is in the bond price notation. Actually, the "Close" is the price per bond in dollars, and the bond has a face value of $1000$, but the price is $104.75$? No, that would be a discount bond, but the price is above par. Wait, maybe the "Close" is the price per bond in dollars, and the bond is a $100$ face value, so $104.75$ per $100$ face, so for a $1000$ face value (which is typical for bonds), it's $10\times104.75 = 1047.5$ dollars per bond. Then, three bonds: $3\times1047.5 = 3142.5$ dollars. Then, commission: $10$ per bond, so $3\times10 = 30$ dollars. Total cost: $3142.5 + 30 = 3172.5$ dollars, which is option c.

Wait, let's verify:

1. Price per ABC bond: $104\frac{3}{4} = 104.75$ (assuming this is the price per $100$ par, so for $1000$ par, it's $1047.5$? No, wait, maybe the bond is a $1000$ par, and the price is $104.75$ dollars? No, that's not right. Wait, maybe the "Close" is the price per bond in dollars, and the bond has a par value of $1000$, so the price is $104.75$? No, that would be $104.75$ for a $1000$ par bond, which is $10.475\%$ of par, which is too low. I think the correct interpretation is that the "Close" is the price per bond as a percentage of par (par = $1000$), so $104\frac{3}{4}\%$ of $1000$ is $1000\times1.0475 = 1047.5$ dollars per bond. Then, three bonds: $3\times1047.5 = 3142.5$ dollars. Commission: $10$ per bond, so $3\times10 = 30$ dollars. Total cost: $3142.5 + 30 = 3172.5$ dollars, which is option c.

Step2: Calculate Cost of Bonds

First, find the price per ABC bond. The close price is $104\frac{3}{4} = 104.75$ (assuming this is the price per bond in dollars, but actually, it's a percentage of par, so par is $1000$, so price per bond is $1000\times1.0475 = 1047.5$? Wait, no, maybe the bond is a $100$ par, so $104.75$ per $100$ par, so for a $1000$ par (10 bonds of $100$ par), it's $10\times104.75 = 1047.5$? No, this is overcomplicating. Let's just use the numbers:

Price per bond: $104\frac{3}{4} = 104.75$ dollars (assuming this is the price per bond, maybe par is $100$). Then, three bonds: $3\times104.75 = 314.25$? No, that's not matching. Wait, the options are $3142.50$, $1047.50$, $3172.50$, $31077.50$. So $3172.50$ is option c. Let's see: $1047.50$ is one bond, so three bonds would be $3\times1047.50 = 3142.50$, then add commission: $10\times3 = 30$, so $3142.50 + 30 = 3172.50$, which is option c. Ah, so the price per bond is $1047.50$ dollars (so the "Close" is $104\frac{3}{4}$ as a percentage of par, where par is $1000$, so $104.75\%$ of $1000$ is $1047.50$). Then, three bonds: $3\times1047.50 = 3142.50$. Commission: $10$ per bond, so $3\times10 = 30$. Total cost: $3142.50 + 30 = 3172.50$.

Answer:

c. $3172.50$