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hello this is my 99th video and helping people study for actuarial exam - to do problem solving for that we're again doing a started problem for point 1.24 like I did in video number 98 we'll be finding the selling price of a bond in video number 98 I introduced Megan's formula for the price of bond here in this problem we will get some practice with it so we will be using that formula it is possible to solve the problem without may comes formula but it is also a problem we're using may comes formula works nicely so we've got a bond with a face and redemption amount that are the same 3000 we assumed F and C the face and redemption and are we the same in the last video to write down that form of Megan's formula we've got annual coupons where the bond is selling an effective annual yield rate which is equal to twice the annual coupon rate okay so here we got a relationship between the yield rate J and the coupon rate r that one is twice the other that's sort of a hint that make-ups formula in the form one of the forms at least that I showed you a lot in the last video is could be useful our over J is going to be a constant the present value of the coupons is equal to the present value of the redemption month the goal is to find the selling price so what did makeups formulas say may comes formula says the selling price P is equal to K where K was the present value of the redemption amount plus r over j r being the periodic in this case annual coupon rate J being the periodic in this case annual yield rate times in parentheses see the redemption amount minus K where again K is the discounted value of the redemption amount C times B sub J to the N where V sub J is the discount factor 1 over 1 plus J all right so let's think about this here we know what are over J is the effective annual yield rate J is twice the annual coupon rate J equals two times R and therefore R over J is R over 2 R is a constant 1/2 so that's one thing that is a hint that maybe makeups formula would be useful let me keep the K unspecified at the moment our over day is 1/2 C is 3000 so we've got C to be 3000 there is now a formula for the price in terms of K can we figure out K well K is C times V to the N that would be 3,000 times V sub J to the N if now we could find B sub J to the end to the N power we can finish this problem so let's see maybe that's a hint that we need to use something that has not been used yet what have we not used yet it's the sentence here the present value of the coupons is equal to the present value of redemption amount we have not used that yet present value of the coupons would be in general F times R times a and J for this problem F is the same as C is 3000 we don't know our we don't know J but we do another ratio let me go ahead and put our in there and put the formula for a m and then yes we can write r over j again like this and once again R over J just like before is equal to 1/2 so this becomes 1500 times 1 minus V sub J to the N and that's supposed to equal the pros and value the redemption amount present value the redemption amount is K is C times V to the N is 3000 B sub J to the n these two things have to equal each other we can solve that equation for B sub J to the N power we can divide everything by 1500 to get to V J to the N equals 1 minus V J to the N therefore V J to the N or 3 times it would equal 1 so VJ to the N will be one third we can now plug that in back up here K is going to be three thousand times one third is 1000 go ahead and write it up here K is going to be three thousand times one third is 1000 and now we can substitute that in here and here to get the final answer for the price the price is going to be one thousand plus one half times three thousand minus one thousand at two thousand two thousand times 1/2 is 1000 1000 plus one thousand is two thousand the final answer for the price the selling price is two thousand do note that that is smaller than the redemption amount which is three thousand here which shouldn't be surprising since R over J is less than one it's 1/2 R is less than J in that situation the price will be smaller than the redemption amount