# Do price approximations lead to arbitrage opportunities?

Do price approximations lead to arbitrage opportunities against a price computed using the exact formula?

For instance, dirty bond price uses a linear approximation to compute the accrual interest: $$P_{d}=P_{c}+\alpha t$$ Whereas the exact formula gives a slightly higher value for $0<t<1$ (with time unit the time between payments), for both continuous or discrete compounding (assuming par): $$P(t)=ce^{i(t-1)}+e^{i(t-1)}P(0)$$ $$P(t)=\frac{c}{(1+i)^{t-1}}+\frac{P(0)}{(1+i)^{t-1}}$$ Giving the high nominal of some bonds, does the difference is ever high enough to produce arbitrage opportunities?