Hello fellows,

I've got a problem to solve and I hope that you will help me (please)!
I want to do a presentation about bonds, their characteristics and bond pricing. I asked my teacher to hand out an assignment and he gave me the Assignment from the book "Investments" BKM 15.16
Thus, here is the issue:

Below is a list of prices for zero-coupon bonds of various maturities.
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Maturity (Years) Price of $1,000 Par Bond (Zero Coupon)
1 943.40
2 873.52
3 816.37

a. An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in three years. What should the yield to maturity on the bond be?
b. If at the end of the first year the yield curve flattens out at 8%, what will be the one year holding-period return on the coupon bond?


And here is the solving:


The current bond price is:

($85x0.94340)+($85x0.87352)+($1,085x81637) = $1,040.20



I do not understand this step!!!
Why do they explain and calculate the bond value like that?

($85x0.94340)+($85x0.87352)+(§1,075x0.81736)=1,040 .20??

I thought I need the required yield, which I will place in the formula for each year! Can someone explain to me this step?

I thank in advance

Lin