 Personal finance practice problem using OneNote. Bond price for multiple bonds. Prepare to get financially fit by practicing personal finance. You're not required to but if you have access to OneNote would like to follow along. We're in the icon left-hand side, practice problems tab in the 11250 bond price for multiple bonds tab. Also, take a look at the immersive reader tool practice problems typically in the text area too with the same name, same number but with transcripts. Transcripts that can be translated into multiple languages either listened to or read in them. We're imagining that we're going to be purchasing multiple bonds at this point in time. So the number of bonds we're going to purchase 120, the face amount of the bond 1,000. This is a typical type of scenario when bonds are issued. They're often issued in $1,000 increments. And if we were to buy the bonds, we might be buying multiple bonds of $1,000 increments. The interest rate or a coupon rate on the bond we're imagining to be 12%. The years to maturity are 20 and we have the semi-annual interest payments that we will be receiving remembering that when we invest in bonds we can basically think of it as though we are loaning money to the issuer of the bond that being the corporation or a government entity in return for in general interest on it which is like the rent on the purchasing power of the money instead of receiving that monthly we usually receive it semi-annually or annually. Then we will also be receiving the face amount of the bond at maturity that lump sum at maturity which you can think about as the principal that we're going to be getting back for the money that we loaned although we might not always be loaning the same amount as the face amount because we might purchase the bond at a discount or a premium. So then we have the market rate. The market rate is something that is not on the bond itself. That's going to be determined by the market and that's going to help us determine how much we're going to be purchasing the bonds for. Now we can apply this market rate on a bond by bond basis or we can think about the multiple bonds that we're going to be purchasing. So one way we can do it to say well what would the price of one bond be and then multiply times multiple bonds or we can try to figure out okay let's figure this all out together as if we're going to multiply out the $1,000 bonds times 120 so we'll do this a couple different ways. So first let's figure out the bond price for one bond. So we're going to take the present value of interest to do that and so there's two formats when we figure out the bond price or two future cash flows is what I mean to say here. One is the series of payments that we're going to receive the interest payments and annuity calculation. The other is the present value of that $1,000. If we take the present value of the annuity payments that calculation in Excel would look something like this. It would be the rate, the rate is going to be the market rate, the 9% that's a yearly rate so we're going to divide it by 2 to get to the semi-annual rate comma number of periods. The number of periods would be 20 but that's annual. We'd have to multiply times 2 to get 6 month semi-annual half-year periods comma the payment would be the $1,000 times the rate, the 12% meaning we would be getting $1,000 times 12% 120 but that rate is usually given on an annual rate even though we're going to get paid semi-annual so we'd have to divide that by 2 meaning we're going to get $60 every 6 months would be the general idea that would give us the $1,10410 then we're going to present value the $1,000 back to the current time period negative present value the rate would be the market rate 9% we're going to divide that by 2 to get the 6 month rate comma the number of periods would be 20 multiplying by 2 to get to the 40 periods comma comma to get to the future value that would be the $1,000 discounting the $1,000 lump sum back that we would get at maturity discounting back at the rate of 9% for 20 years or 40 semi-annual periods gets us to the $171.93 if we add that up the bond price we would expect to be $1,276.02 noting that is issued at a premium something higher than the face amount of the bond that's because the market meaning if we bought bonds similar bonds we can only get 9% return and this bond when it was issued when it was made had a 12% return on it therefore we would be willing to pay more for it to compensate we can't adjust the interest rate in other words we can't adjust the rent payments on the money that we are loaning it because it's on the bond already what we can do to compensate is adjust the price buying the bond in this case at a premium so then we could just multiply that that's for one bond times 120 which would mean that we would then have 153 123 in terms of the total bond price that's one way we can do it now you could also do it this way you could say all right well if I have 1000 bonds 1000 1000 120,000 dollar bonds 1000 times 120 is 120,000 and you might see this in like book problems where they say the bond is 120,000 oftentimes one bond isn't 120,000 but you're investing 120,000 in bonds which might be broken out into 1000 dollar increments 121,000 dollar bonds but we can do that we can do the calculation on this 120,000 here and we can say okay the present value of the interest payments would then be negative present value the rate is still the market rate at the 9% divided by two and then we've got the number of periods the number of periods is still 20 times to to get to 40 and then we've got the amount that that is going to be the payment is the is the payment and that is now 120,000 times point one that would be for a year divided by two or you can think of it as each bond is going to have 1000 dollar bond times point one two that would be the yearly amount divided by two that would be how much we're going to be getting every six month for one bond times 120 would give us once again for all of the bonds if we present value that we get to the 132 491 if we present value the face amount which is not now 1000 but rather 120,000 can take the negative present value of the rate which is going to be the 9% divided by two number of periods would be 20 times to comma comma future value instead of 1000 for a single bond it's going to be the 120,000 discounting it back adding that up we once again get to the 153 123 so remember whichever way you do it just remember that when you're often times the bonds will be an increments of like 1000 or like 100 or something like that and you're probably going to be buying multiple bonds and so you can calculate things based on one bond because they're similar in increments if they're all the same bond the same issuance type of the bond then you might be able to multiply it out to get the total price or you can you can try to look at it this way in terms of figuring the face amount for all the bonds that you might be purchasing and calculate the present values on them again assuming that they're all like bonds they all have the same conditions they're all $1000 bonds interest at 12% same maturity date same market rate.