Suppose that household resource constrain equation is as follows: $$P_tC_t + Q_tB_t+ P_tI_t \leq W_tL_t+R_tK_t+B_{t-1}+D_t$$ where $P_t$ is price at time $t$, $Q_t$ is the price of one bond quantity, $B_t$ is bond quantity, $I_t$ is investment, $W_t$ is wage, $L_t$ is labor amount, $R_t$ is nominal capital rental rate, $K_t$ is capital at tie $t$, $D_t$ is dividends.
Taking it into Lagrangian at $t=0$: $E_0 \sum_{t=0}^{\infty}\beta^t U(C_t,L_t) - \lambda_t[P_tC_t + Q_tB_t+ P_tI_t - (W_tL_t+R_tK_t+B_{t-1}+D_t)]$
Taking partial derivative of lagrangian respect to $K_{t+1}$ where $K_{t+1} = (1-\delta)K_t + I_t$ seems to produce: $$\frac{\lambda_t}{\lambda_{t+1}} = \frac{R_{t+1}}{P_{t+1}}$$ (Dropped expectation sign, but should be there)
And taking partial derivative of the lagrangian respect to $B_t$:
$$\frac{\lambda_t}{\lambda_{t+1}} = \frac{P_t}{P_{t+1}}\frac{1}{Q_t}$$
Equating these two,
$$R_{t+1} = \frac{P_t}{Q_t}$$
Taking $-\log Q_t = i_t$
$$\hat{R_{t+1}} = \hat{P_t} - \hat{Q_t} = \hat{P_t}+i_t$$ where $\hat{X} = \log X$.
This does not seem to be a right formula to me, and I must have made some mistake. What did I do wrong here?