Pricing zero coupon bonds on a yield curve

I'm getting confused about how I should price the current price of a zero coupon bond when there are several yields to choose from. For instance, lets say that there is an upward sloping yield curve. The rates are $r_1 < r_2 < \cdots < r_{10}$.

Typically, when we price the current price of zero coupon bond that matures in 1 year, the calculation is simply $$P = \frac{100}{1 + r_1}$$ However, when we price the current price of a 10 year zero coupon bond, I feel that it is overly simplistic to calculate the price as $$P = \frac{100}{(1+r_{10})^{10}}$$ Rather, I feel that the correct way to price this is to think the rates as forward rates for each year so that $$P = \frac{100}{(1+r_1)(1+r_2) \cdots (1+r_{10})}$$

Any input will be much appreciated. Thanks in advance.

• The yield curve can be expressed in several ways. What are these $r_i$s ? ZCB rates or forward rates? Where did you get them? If ZCB rates then the 1st answer, otherwise the secon. – Alex C Apr 3 '17 at 0:03
• There is even a third possibility the $r_i$s could be the "par rates". – Alex C Apr 3 '17 at 0:41