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When we refer to "quoted price" of bond, or "clean price", it is equivalent to refer to his "present value" or "theoretical value", which corresponds to the price that I invest in the bond?

For example, for a fixed coupon bond $C_t$, it is given by: $$P=\sum_t\frac{C_t}{(1+r)^t}+\frac{VR}{(1+r)^n}$$ where VR is the nominal value of the bond and r is the rate of yield

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The "clean price" of a bond has a technical meaning. It is the invoice price of a bond (which is what your formula refers to), less the accrued interest. (The invoice price is the total dollar amount you pay when you buy a bond.)

The invoice price of a bond is mapped to the yield using the formula you give. Yes, this is equivalent to an internal rate of return. (There may be small technical differences between a bond yield than an internal rate of return; bond yields have a slightly more complex quote convention. Your formula is only an approximation.) It is a "quoted price" if the price comes from some source of market pricing. Most price quotations refer to the clean price; you need to add accrued interest to get the invoice price.

This would not normally be called a theoretical price, it is just a straightforward application of a pricing formula.

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