Coupon: 500,000 * 0.09/2 = $22,500
n = 13 years * 2 times per year = 26
i = 0.08 / 2 = 0.04
PV of the coupons: use PV ordinary annuity "PVoa"
PVoa = PMT [(1 - (1 / (1 + i)^n / i]
= 22.5k[(1 - (1/1.04^26)) / 0.04]
= 22.5k[(1 - 0.36069) / 0.04]
= 22.5k[15.98277]
= $359,612.31
PV of par paid at maturity
PV = FV / (1 + i)^n
= 500,000 / 1.04^26
= $180,344.60
Add the two together = Price: 539,956.91
If an annual pay bond...
Coupon = 500k *0.09 = 45k
n = 13
i = 0.08
Price = 539,518.87
Sorry, that's as close as I could get.
First, find out the annual interest that the bond holder will receive. The amount is 9% of 500,000 = $45,000. The bond holder will receive this amount for 13 years now onwards. So, it is an annuity for 13 years. Calculate its present value. The discount rate should be 8%, not 9%. From the table, the PVIFA is 7.904. Multiply it with the annual interest amount $45,000. This is one component of your present value.
Apart from this annual interest, bond holder will also get principal amount at the end of 13 years. The present value of that amount should also be considered. From the table, the present value factor for that amount is 0.368. Multiply it with the face value of the bond $500,000.
Take total of both of these. [45,000*7.904] + [500,000*0.368]. You should get your answer. The answer with this method is $539,680 which is close to the correct answer. Instead of using values from the table, if you use the relevant formula, you will get the accurate answer.
Is this another test question? In the real world you need to go back to the author of this financial puzzle and question how he/she arrived at a "correct answer" when the closing question states, "the investor should expect". Any time you're holding an instrument which is dictating an annual percentage rate above market you get your asking price. In the case you've described a seller could easily ask $600,000.
I guess what I'm saying is this; the info you're dealing with isn't really providing you with a decent return on your education. Having said that, stay with your first answer. (Private Banker)
An investor purchased $500,000 of 15-year bonds, with a contract rate of interest of 9%, payable annually. After holding the investment for 2 years (13 yrs left), the investor wants to sell it now that the market rate for such securities is 8%. What is the price the investor should expect to get when selling this bond?
The correct answer is $539,520, but I have no idea how to get that answer.
I would greatly appreciate your help
