# How do you calcualte Yield To Maturity, given only the coupon rate and current required rate of return?

Suppose today a 10 per cent coupon bond sells at par. Two years from now, the required return on the same bond is 8 per cent. What is the YTM?

^That's a question I've been asked and have literally no clue about how to calculate the YTM.

My understanding is: YTM is the anticipated return on a bond if held to maturity. If I buy a fresh bond at say \$90 and the par value is \$100 at 10% coupon rate, the YTM will be 10/90 = 11.11%. So for this question, If I buy a bond on the secondary market at par value, the YTM should equal the coupon rate no? If so, how does rrr affect YTM?

I'm so confused, send help.

The calculation form depends upon the coupon frequency of the bond. For an annual coupon, if we denote the yield as y, then the price of the bond equals (convention of \\$100 equals par): $$p = \sum_{i=1}^8 \frac{10}{(1+y)^i} + \frac{100}{(1+y)^8}.$$